The West German government continued its test of wills with terrorists today and let two deadlines go by that could have meant death for 87 hostages on a hijacked airliner and a kidnaped industrialist. The government showed no signs of giving in to demands that 11 other notorious terrorists be freed from West German jails.

Just 40 minutes before the deadline when the hijackers said they would blow up the plane with passengers and crew aboard, the four terrorists ordered that the plane take off after two days in the sweltering heat on a runway in the tiny Persian Gulf state of Dubai.

The hijackers, at least two of whom speak Arabic, ordered the pilot to fly to Aden, South Yemen, a country on the southwest corner of the Arabian Peninsula ruled by an extreme leftist government that has harbored released West German terrorists in the past.

The hijackers had repeatedly threatened to blow up the Lufthansa Boeing 737 and its passengers and crew unless the government in Bonn met its demands for the release of the 11 jailed terrorists, two Palestinians in Turkish jails and $15 million in ransom money. The deadline was set for 8 a.m. EDT.

Late tonight, Yemoni officials said that they had refused permission for the plane to land but that it had come in anyway, landing on sandy ground alongside the main runway.

The officials said they told the bijackers that they would not be allowed to stay and the plane was refueled to allow it to leave.

The hijackers' leader, who identifies himself as "Martyr Mahmoud," told the Dubai control tower before take off that "the West German government and (Chancellor Helmut) Schmidt are personally responsible for what happens to the hostages. We have given them 60 hours and they have done nothing."

Earlier in the day, Bonn had also let a deadline go by that had been contained in another ultimatum with the same demands from the kidnapers of industrialist Hanns-Martin Schleyer.

As of tonight, there was no indication whether the kidnapers had carried out their threat to kill him.

Schleyer was kidnaped Sept. 5 by terrorists demanding release of 11 of their jailed comrades - all of them among the most notorious in West Germany and including three surviving leaders of the Baader-Meinhof gang. The Schmidt government had successfully resisted those demands, but the hijacking of the Mallorca - Frankfurt jet over the Mediterranean Thursday dealt a vastly more powerful hand to the two groups and has put enormous pressure on the government.

Still, Bonn has not yielded and spokesman Klaus Boelling said today that the government did not believe that hope of saving the hostages had evaporated by the expiration of the deadlines. He said Bonn was still pursuing all realistic possibilities of freeing the hostages.

The hijackers have consistently refused to free any of the 82 passengers, despite appeals to allow at least nine women, seven children and two reportedly seriously ill persons to disembark. Two Americans, 44-year-old Christine Santigo of California and her five-year-old son are reportedly among the passengers.

South Yemen is one of the three countries that the terrorists have demanded the prisoners be flown to if Bonn releases; them. The others are Vietnam and Somalia.

Although all three countries have indicated they would not accept any freed prisoners, in March, 1975, South Yemen did provide haven for five other jailed anarchists in West Germany who were freed in return for the release of the West German kidnapers of West Berlin political leader Peter Lorenz.

Several of those five subsequently filtered their way back into West Germany's urban guerrilla scene and are now back in jail after new jets of terrorism.

That was Schmidt's first encounter with terrorists as chancellor, but a few months later, when anarchists took over the West German embassy in Stockholm, Schmidt took a tough line and refused to free any more prisoners.

All the terrorists are part of the extreme leftwing "red army faction," the name used by the followers of the Baader-Meinbof gang.

Here in Bonn, the situation grows ever more tense. Schmidt and his crisis staff meet several times a day, with calls of support coming in from French President: Giscard d'Estaing and British Prime Minister James Callaghan.

Unless the hijackers give up, Schmidt faces a basically no win situation. If the hostages on the plane are killed without any action on Bonn's part, it could have a serious political blacklash both among those who feel the government should have freed the prisoners and among those who say they feel "frustrated" that West Germany, unlike the Israelis in the Entebbe rescue raid and the Dutch in the train hijacking last spring, should at least have attempted to "do something" rather than remain passive.

On the other hand, the release of jailed terrorists - especially the leader, Andreas Baader, who symbolizes the band of anarchists that is despised and rejected by the overwhelming majority of West German citizens - could also have severe repercussions for the future of Schmidt's coalition government.

Meanwhile, the West German federal constitutional court today ruled against an eleventh-hour appeal by Schleyer's family to force the government to give in to the terrorists' demands. The suit was based on the consituation's requirement that the state protect the lives of its citizens.

The court, meeting in an extraordinary session late last night in Karlsruhe, ruled just hours before the kidnapers' ultimatum was to expire, that the government also had a responsibility to protect the society as a whole. An affirmative decision, it said, would have tied the government's hands in all future cases. It said that responses to terrorist violence had to be dealt with on a case-by-case basis.

Schleyer, 62, was the head of both West Germany's employer and industrial federations. A powerful figure in the business elite and as an adviser to Schmidt, he was a perfect target for extremists, who branded him "the fat magnate" of an economic system that they want to destroy.

The lawyer-turned-industrialist was also a Nazi party member and SS officer during World War II, which his captors apparently also reasoned would make him less of a sympathetic character to the general public.