Beirut — On many public buildings in east Beirut and in the coastal cities of Sidon and Tyre is a glamorous photo poster of a curly-haired young man in military fatigues with his legs crossed. He is cradling a rifle.
He is Bashir Gemayel, political and military leader of Lebanon's Maronite Christians. And he is the man Israeli officials openly back to become the next president of Lebanon. Israel expected him to throw his extensive military forces into the battle to help the Israelis evict the Palestine Liberation Organization from west Beirut.
But the wily Mr. Gemayel, a tough young lawyer and combatant, has surprised both Israeli friends and one-time Lebanese Muslim foes by carefully distancing himself from Israeli military action while conspicuously courting Lebanese Muslim and other Arab leaders, even some who once opposed him and backed the PLO.
In the tortured maze of Lebanese politics, such a carefully charted course has made Mr. Gemayel a much more formidable candidate than had been expected for the perilous job of trying to lead Lebanon back to unity and stability.
Mr. Gemayel heads Lebanon's largest private army, estimated at anywhere from 10,000 to 25,000 men. It is commonly known as the Phalangists, after the party founded 43 years ago by his father, Pierre, an admirer of Franco's Spain. Mr. Gemayel's supporters now play down this name because of its fascist connotations. They prefer the name ''Lebanese Forces.''
As non-Muslim religious minorities in a Muslim-Arab world, Israel and the Maronites had much in common. For the past six years Israel quietly backed the Lebanese Forces with a reported $100 million in arms and military aid to fight the Syrians and the PLO.
The Lebanese Forces were delighted when Israel invaded Lebanon. They have called for the Israelis to finish the job of driving out the PLO. But Mr. Gemayel, who very much wants to become president of Lebanon, quickly realized that he had to distance himself from the invaders if he was to win the majority of the 99 parliamentary seats and thus become president.
Moreover, he was more sensitive than the arriving Israelis to the position of the wealthy Maronite community as commercial and banking middlemen of the Arab world. That position would be jeopardized if they isolated themselves by open alliance with Israel.
''Some Western media didn't understand the character of Gemayel,'' says Naoum Farah, a lawyer who heads the foreign relations department of the Lebanese Forces command. ''They labeled him a gunslinger, but we don't have cowboys here. We told our Muslim compatriots that we wouldn't participate in the taking of west Beirut.''
Mr. Farah openly opposed a long-term Israeli stay in Lebanon. ''We have an independent policy,'' he said, ''which calls for withdrawal of all foreign forces from Lebanon. We will not accept any agreement which leaves either the Syrians or the Israelis in Lebanon.'' Asked if he would call Israel his ally, Mr. Farah replied, ''No comment.''
To enhance his statesmanlike image and to calm Arab fears of a separatist Maronite state, Mr. Gemayel traveled to Saudi Arabia in early July. ''This was a major step,'' Mr. Farah says. And, in an attempt to find a mutually acceptable basis for a solution in Lebanon, Mr. Gemayel met on July 17 with Walid Jumblatt, titular head of the Lebanese leftist forces. Mr. Jumblatt's late father was the PLO's key ally and a bitter enemy of both Mr. Gemayel and his father.
But Walid Jumblatt has spoken respectfully of Mr. Gemayel in recent days, and Mr. Farah insisted that ''common ground'' existed between the two men. This, he said, was based on the principles of ''the unity of Lebanon'' and ''the sovereignty of Lebanon over all residents,'' a catch phrase for central government control of all factions, including any Palestinians who remain.
Although the results of Mr. Gemayel's moves - and indeed the probability of Lebanese elections being held as scheduled this summer - will be clearer once the siege of Beirut is lifted, many obstacles are already apparent. For example:
* Mr. Gemayel will have to come to terms with Muslims of the Shiite sect, a growing bloc of nearly 1 million Lebanese who are pressing for more political power. Key political offices in Lebanon are allotted by religious sect, with Maronites guaranteed the presidency.
Mr. Farah suggested that Shiites might one day demand the prime minister's slot now allotted to numerically fewer mainstream Sunni Muslims, a question he recommended should be worked out within the Muslim community. ''It would be hard to change that now,'' he added.
* Mr. Gemayel may face opposition from other Christian leaders. Former President Camille Chamoun, whose private army was ''absorbed'' into Gemayel's forces, told German television he did not believe Gemayel could win the presidency. In south Lebanon, Israel is backing the separate enclave of former Lebanese Army Maj. Saad Haddad with whom Farah stressed the Lebanese Forces ''have no relations.''
* Mr. Gemayel may have to restrain his forces from trying to settle old scores as they tried to do with the Druze minority before the Israelis stopped them.