Strikingly, 28 percent of those who said they voted for President Reagan in 1984 said they preferred Mr. Dukakis over Mr. Bush this time; only 9 percent of those who said they backed Walter F. Mondale in 1984 switched to Mr. Bush. Mr. Dukakis was also far ahead among those who said they did not vote in 1984, and he scored well even in groups where President Reagan continues to be popular - notably among voters under 30 years old.

One reason why Mr. Reagan's personal popularity may not helping Mr. Bush very much is that voters said that his Administration had performed poorly on key issues, notably drugs, which was named the nation's most important problem by 16 percent of the entire public, more than named any other. Democrats generally and Mr. Dukakis in particular were seen as more likely to deal with the problem effectively than were the Republicans and Mr. Bush.

Polls taken six months before ELection Day cannot be taken as predictive of the ultimate election outcome. Robert Teeter, Mr. Bush's poll taker, said that polls taken now may be overestimating Mr. Dukakis, since voters know little about him except the largely favorable news that he has won a a string of primaries since March. In the latest survey, Mr. Dukakis led his only remaining opponent, the Rev. Jesse Jackson, by a margin of better than 3 to 1 among Democratic primary voters.

In theory, a poll taken among as many people as were involved in this one should accurately reflect public opinion within three percentage points in either direction.

The survey did contain some hopeful signs for Mr. Bush and the Republicans.

Many voters, for example, worried that Mr. Dukakis may lack the exprience to be President, and the electorate as a whole sees Republicans as safer than the Democrats on foreign policy and defense.