While Gov. Michael S. Dukakis made a strong showing in a recent presidential preference poll of New Hampshire voters, political anaylsts said the race is wide open and the Massachusetts chief executive will have to broaden his national image if he wants to maintain his early popularity.

The poll released last Friday by the Boston Globe, showed Dukakis with 41 percent of support, closely followed by former Colorado senator Gary Hart, who received 38 percent of support.

The other Democratic candidates trailed far behind the two leading contenders. The poll had a margin of error of six percent.

The poll, conducted by Kennedy School Associate Professor of Public Policy Gary R. Orren and MIT lecturer Peter H. Lemieux, was based on a random survey of 741 New Hampshire voters several days after the governor announced his candidacy last month.

Many Bay State political analysis said the results of the poll were not unexpected. They said that because Massachusetts borders on New Hampshire, local television and press coverage of the governor's activities generated support for Dukakis.

In addition they cited the governor's particular attention to the concerns of New Hampshire residents.

Dukakis "is governor of a neighboring state and many [New Hampshire] residents feel that he is one of their own he understands their needs," said Orren.

Dukakis' stand against the New Hampshire based Seabrook nuclear power plant has also won him the support of many of the state's residents, political observers said.

But because Dukakis has had such close political contact with New Hampshire voters, some analysts said that theresults of the poll indicates strong regionalsupport that is not indicative of nationalsentiment.

"The poll reflects the influence of the Bostonmedia, and the results create the sense that[Dukakis] is a real contender, but he will be hard-pressedto keep his strong standing in New Hampshire,"said Jan Smith, an assistant political consultantfor the consulting firm Marttila and Kiley thatsupports presidential candidate Sen. Joseph Biden(D-Del.)

"It will be a question of maintaining his lead,but it may raise false hopes," she said. "He willhave to concentrate on building support on anational level," Smith said.

The governor's campaign office said thatDukakis was "gratified" by the strong support thepoll showed he had among New Hampshire voters butadded that he is cautious.

"It is too early and polls will go up and down.We have a great deal of hard work to do to earnthe support of the people of New Hampshire and thecountry, and the governor intends to works as hardas he can to do that," said Dukakis's ActingCampaign Spokesman Steven. J Akey.

While Hart did almost as well as the governor,the Coloradan's New Hampshire campaign headquartersaid that they generally do not think polls aresignificant because presidential races have atendency to fluctuate.

Nevertheless, they were pleased with the poll'sresults, and said the Hart has maintained strongsupport among voters in New Hampshire andthroughout the nation, while Dukakis has not..

"He should be well known in New Hampshire, buthe's not registering well in national polls," saidHart's New Hampshire Campaign Director Susan S.Categari. "He will have to show a lot of namerecognition throughout the U.S. that will be thereal test," she said.

Dukakis has been traveling to key politicalstates in recent weeks, an has made the pledge toappear in Iowa every two weeks, and New Hampshireevery week to try to build support