3 Updated question regarding Joel Ethertons answer.
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You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'grey hat' option to circumvent this restriction (though the latter will likely bewill likely be possible somehow as usual seems indeed possible somehow as usualper Joel Ethertons answer - make sure to read my comment as well though ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).

You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'grey hat' option to circumvent this restriction (though the latter will likely be possible somehow as usual ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).

You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'grey hat' option to circumvent this restriction (though the latter will likely be possible somehow as usual seems indeed possible as per Joel Ethertons answer - make sure to read my comment as well though ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).

2 Fixed typos.
source | link

You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'gray'grey hat' option to circumvent this restriction (though the latter will likely beenbe possible somehow as usual ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).

You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'gray hat' option to circumvent this restriction (though the latter will likely been possible somehow as usual ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).

You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'grey hat' option to circumvent this restriction (though the latter will likely be possible somehow as usual ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).

1
source | link

You are aware already that this is not intended according to the regulations outlined in Article 4 of the respective EC regulation 733/2002:

  1. The Registry shall:
    [...]
    (b) register domain names in the .eu TLD through any accredited .eu Registrar requested by any:
    (i) undertaking having its registered office, central administration or principal place of business within the Community, or
    (ii) organisation established within the Community without prejudice to the application of national law, or
    (iii) natural person resident within the Community

I'm not aware of any official/legal way to achieve what you desire, neither of any 'gray hat' option to circumvent this restriction (though the latter will likely been possible somehow as usual ...).

So I'm afraid that depending on you concrete needs your will need to either establish an official undertaking within the Community or at least contract with an affiliate who is resident in the EU (i.e. someone who is not just performing the registration on behalf of you, rather is a real business partner and willing to take legal responsibility regarding the domain ownership as such!).