@Walter Hinteler,
Well, I searched a bit:
The European Community's first reaction to the Greek application was initially expressed by the European Commission, which, according to article 237 (at the time) of the Treaty of Rome, had to state its "opinion" on the country's application for accession to the Community.
The Commission published its "opinion" on January 28, 1976.
It proposed the institutionalization of a pre-accession transition period before full institutional integration, in order for the necessary economic reforms to take place but said as well that a "clearly positive response" should be given to Greece's request for accession.
Especially due to the pressure of Germany (and France) more accession negotiations were initiated in July 1976 and brought to a conclusion in May 1979.
Finally, on 1 January 1981 Greece becomes 10th member of European Community.
All EC-members became automatically EU-members with signing/ratifying the Rome Treaty (as well as the Maastrich Treaty respectively Lisbon Treaty years later).