In Cheers they said that Frasiers father was a chemist and that he died. I guess they ignored that when they made frasier!

Actually in one of the episodes of Frasier, I think Martin teased him about telling the people back in Boston that he was dead. Apparently Frasier was ashamed of his father back then, so he made up the story that he was dead, so that he wouldn't have to talk about him.

I think it was the first episode when Sam Malone visited Seattle.
When Sam meets Martin, he mentions that Frasier had told everyone his father was dead.
Frasier explains that he was angry at Martin at the time, so he made up the story about him being dead.

TJL, I believe you are right, you have a very good memory, because I wasn't sure if it was during Sam's visit or during Woody's visit. But thanks for clarify that for us.

I have a question about Frasier's Mother.
On Cheers, she made an appearance and tried to break up her son and Diane, even trying to bribe Sam to get back together with Diane.
Yet, on "Frasier," the Mother has been deceased, and judging by they way they talk about her, she passed away some time ago.
Was it ever esablished when Frasier's Mother died?

I'm not exactly sure but it was probably before frasier and lilith got married.

She definately died during the Cheers years because he mentioned it on a Cheers episode. Also don't forget that John Mahoney(Martin Crane) was on an episode of Cheers. Not as Martin, but a guy who wrote commercial jingles!