Brain-Teaser 509

From The Sunday Times, 14th March 1971 [link]

Alpha, Beta, and Gamma are brothers. One of them always tells the truth, one always lies, and the other sometimes tells the truth and sometimes lies.

I asked Gamma who was the elder of Alpha and Beta. Gamma (who was a little shy) whispered the answer to Alpha who the told me that Gamma had said that Alpha was older than Beta. Beta agreed that he was younger than Alpha, but he warned me that Alpha did not always tell the truth.

The eldest of the three said that Gamma was more honest than Beta, and the youngest agreed with him. Furthermore, the younger of Beta and Gamma said that Alpha always told the truth.

Who is the eldest? And who is the most honest?