* Relations between the Palestine Liberation Organization (PLO) and Syria are growing more strained, several Arab sources have reported in recent days. Palestinian officials, they say, blame Syria for a recent attempt to smuggle guns into Austria and for the assassination last month of the French ambassador to Lebanon. The PLO also is experiencing a potentially troublesome division with one of its important member groups, the Damascus-based Saiqa organization. Compounding current problems for the PLO have been the recent car bomb explosions in predominantly Palestinian areas of Lebanon.

* Military activity is increasing along the remote Chad-Sudan border, and a power struggle between Libya and Egypt may be to blame. Libyan-backed Chadian forces and rebels supported by Sudan and Egypt recently fought for control of the Chadian town of Adre. Chad has charged in recent days that Sudanese and Egyptian irregulars were taking part in the fighting.

There are an estimated 5,000 Libyan soldiers shoring up the Chad government of Goukhouni Woddei. Western political analysts in the Middle East believe Egypt is stepping up its activity along the Sudan-Chad border in an attempt to tie down Libyan leader Muammar Qaddafi's forces. Egyptian Vice-President Hosni Mubarak flew to Washington Oct. 1 to brief the Reagan administration on the situation along the Chad-Sudan border.

* Now that the heat of summer is fading, Iran and Iraq are stepping up their war. Iran last week reported a major breakthrough at the Iraqi-besieged oil city of Abadan. Iraq denies the claim, but has reported withdrawal of its troops from the east to the west bank of the Karun River. The increasing intensity of fighting has begun arrousing concern in the Middle East that the war, contained so far, could spread.

* Would an Israeli-Jordanian confederation work? Israeli Prime Minister Menachem Begin told Israeli interviewers last week that such a confederation was his "dream." But Jordan's information minister called Mr. Begin's dream "pure nonsense."

Jordan has been miffed also by the new Begin government's contention (stated frequently by Defense Minister Ariel Sharon) that Jordan, with 60 percent of its population Palestinian, already is the "Palestinian state" that the Arabs seek.

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