AUSTIN (AP) -- Democratic Sen. Edward Kennedy took advantage of a Texas fund-raiser to offer some political advice to Republican presidential hopeful Gov. George W. Bush.

''The one thing that bothers me about George W. is a young man getting along on the basis of a famous family name,'' Kennedy said. ''I've got news for him: It's not going to work.''

''I had to get out there, I had to get right out there and start right at the bottom,'' Kennedy quipped over the audience's laughter.

The long-time Massachusetts senator is the brother of former President Kennedy and Attorney General Robert Kennedy, both of whom were assassinated. Edward Kennedy failed in his bid for the White House in 1980.

Bush, the son of former President Bush, rarely, if ever, talks about his father on the campaign trail.

Kennedy took light hits at the governor while visiting Bush's home state, but stopped short of turning his appearance into an all out anti-Bush rally.

''I'm not down here going after that,'' Kennedy said. ''But I would hope in the course of the campaign ... that he's going to be able to explain to the people of this country about why you've got more people who are uninsured for health insurance here in the state of Texas than any other state in the country.''

Bush campaign spokesman Scott McClellan said Kennedy has supported the governor in the past and that some of Kennedy's criticisms were not entirely accurate.

Kennedy said the strong state record Bush has touted on the campaign trail can partly be credited to Democrats and others in Texas who have worked to increase the quality of education and protect poor children.

''I thank the Democrats down here who are trying to do something about children in the state of Texas,'' Kennedy said.

''We appreciate that Sen. Kennedy recognizes that Texas is on the leading edge of education reform under the leadership of Gov. Bush,'' McClellan said.

McClellan said Bush worked closely with state legislators in implementing the Children's Health Insurance Program that will insure 423,000 Texas children by 2001. Bush also has supported other children's initiatives such as the Texas Healthy Kids Organization, he said.

Kennedy spoke to about 200 members of the state Democratic Party at a luncheon in Austin before visiting with former first lady Lady Bird Johnson at the Lyndon Baines Johnson Library.

Kennedy called on the party to work together and elect Democrats at all levels of government.

''I do think these next months are very, very important in terms of the future of our country,'' Kennedy said, adding that he believed there was a good chance Democrats would take control of Congress after the next election and that former New Jersey Sen. Bill Bradley and Vice President Al Gore are capable presidential candidates.

''I think it is extraordinarily important, and it is important as well in terms of the presidency. I think we have the candidates that can be successful now,'' Kennedy said.