Gov. Dolph Briscoe, who claimed his minimal approach tostate government has contributed to one of the most prosperous periods in the state's history, has apparently lost in his bid to serve an unprecedented 10 years as Texas governor.

John Hill, the state's activist attorney general who has challenge some of the state's powerful interest groups, handily led Briscoe after Saturday's Democratic primary. But as unofficial returns continued to be counted, it was unknown whether Hill's 50.6 percent share of the vote would hold - and thus keep the two out of a runoff.

Late yesterday, Briscoe had still not conceded the election to Hill, who campaigned on a platform of better, more active government with no new taxes. Briscoe's apparent defeat came despite a $3 million campaign that was financed, in part, with $1 million in loans from state banks secured by bankers, oilmen, farmers and other businessmen.

If Hill margin holds, he will face Republician William Clements, an oilman and former Denfense Department official who defeated former state party chairman Ray Hutchinson for the GOP nomination.

The election was seen by many as a referendum on Briscoe's 5 1/2 years in office - a period marked by his frequent absences from the capital and his apparent inability to successfully speak for Texas on national issues.

But it was also a time of economic emergency for Texas - now the third most populous state - which saw tens of thousands of people move here to take advantage of plentiful jobs and comparatively low taxes.

It is "obvious" Texans are ready for a more active governor, said Democratic national committeewoman Billie Carr, a Houston liberal who supported Hill. "I've always said that if Texans wanted a governor, they'd elect one."

Briscoe was also apparently vulnerable to an informal Texas tradition that governors serve no more than six years. (Until 1974, Texas governors were elected to two-year terms.)

Too, Hill, who had rushed to the aid of striking farmers arrested during a border protest, did relatively well in the state's rural areas, a traditional source of Briscoe votes.

Rep. Robert C. Krueger, a conservative Shakespearean scholar from New Braunfels who earned instant stature in the House with his fight to decontrol oil and gas prices, soundly won nomination face Republican incumbent John G. Tower in November for his Senate seat.

Whatever happens in that 1979 race in November, the 24 member Texas House delegation - whose 1979 retirements include the four most senior members, with 151 years of service - was faced with still more turnover.

Rep. Dale Milford, a Democrat from Grand Prairie, conceded defeat to Martin Frost, a liberal who ran Jimmy Carter's campaign in North Texas in 1976 and won 56 percent of the vote Saturday. And Rep. John Young, a Corpus Christi Democrat accused in a Capitol Hill sex scandal last year, lagged in the voting with 38 percent to state Rep. Joe Wyatt's 41 percent, but a third candidate drew enough votes to force Young and Wyatt into a June 3 runoff.

A defeat for Young would mean that eight seats - one third of the state's traditionally cohesive and powerful House delegation - would change hands when the 96th Congress convenes in January.

Clements' victory means that two Ford administration officials will be on the ballot in November in Texas, a state generally considered crucial to efforts to strengthen the Republican Party. James A. Baker III, who served in the Commerce Department and ran President Ford's 1976 election campaign, was unopposed in the race for the Republican nomination for attorney general.

Baker will face Democrat Mark White, who upset Price Daniel Jr., former speaker of the Texas House and son of a former governor.

Former governor Preston Smith ousted by Briscoe in the 1972 Democratic primary, finished a distant third in the five-way Democratic race.

With voting returns incomplete in some 50 small rural counties and in the EI Paso area, HILL, whose campaign cost about $1.4 million, was barely over the 50 percent mark, while Briscoe had about 42 percent. But as unofficial counting continued last night, there were no clear trends that pointed to a possible runoff.