A "deepening socialist democracy" was proclaimed by General Secretary Leonid Brezhnev when he presented the draft of a new constitution to the spring plenum of the party Central Committee last Tuesday. But even as he spoke, events intimated that rule in the Kremlin still smacks less of constitutional order than of push and shove.

For besides approving the draft constitution "in main," the plenum also decided to demote a veteran Soviet leader, President Nikolai Podgorny. That decision, made in secret without any explanation, came amidst signs of acrimony that loosed a flood of rumors about the Soviet leadership.

Behind all this there lie the anomalies imposed by Soviet politics on Soviet history. Each new leader has rewritten the story of the past, magnifying his own achievements by undoing or co-opting thise of predecessors. When Brezhev reached the top, he too faced the task of ensuring his place in history.

A new constitution offered one obvious device. The last Soviet constitution, put through in 1936 by Stalin, was famous for the contrast between rights ensured in theory and arbitrary rule carried out in practice. Still it was known through thick and thin as the "Stalin constitution."

The idea of a new, more with-it constitution was first proposed by Nikita Khrushchev at the 22nd Party Congress in 1961. Brezhnev picked it up after the fall of Krushchev and made the idea his own. He pushed hard and repeatedly for a draft, and it seemed likely that one would be surfaced at the 25th party congress in February 1975.

Certainly the innovations so far announced seem innocuous enough. There will be less emphasis on class struggle and ethnic autonomy within the Soviet Union and on confrontation with the world outside Russia. A new section on rights will feature such socialist standbys as the right to a job, a decent education and medical care.

But giving up such slogans as "dictatorship of the proletariat" and "capitalist encirclement" apparently drew bitter opposition from the ideological watchdogs led by Mikhail Suslov, a senior party secretary who seems to stand second to Brezhnev in the Soviet pecking order. The opposition delayed approval of the new constitution beyond the 25th congress.

Brezhnev then set his sights on the 60th anniversary this fall of the Bolshevik Revolution. He apparently won Suslov's approval of a draft quite recently. A mark of Suslov's okay, said to be in keeping with his wry sense of humor, is that he delivered to the plenum last Tuesday a report on the new words and slightly new music to be adopted for the self-adulatory and militantly combative national anthem, which Stalin caused to be written in 1943.

According to those present, discussion of the new consitution at the plenum was "businesslike and orderly." But backstage there was trouble over a decision to drop Podgorny as a member of the Politburno, a step that in effect strips him of his role as head of the Supreme Soviet, or legislature, and President.

It was the announcement that signaled the troubled: Unlike any similar announcement - including that of Khrushchev's ouster - this one came without the usual polite fictions of health, age or retirement.

Podgorny is 74 and has long been known as a figurehead, unconnected with either the Brezhnev faction in the leadership or the Suslov group. So almost certainly the reason for the shabby treatment is that he refused to go quietly. But why did Brezhnev bother to drop a figurehead? That question set Moscow agog with speculation early last week, and yielded three rough theories.

One was that Brezhnev wanted to be both general secretary and president. In that way he would couple the real and the formal power and deepen further his claim to historic stature.

A second theory was that Brezhnev wanted the job to accommodate or weaken one of the "watchdog" factions under Suslov - perhaps Prime Minister Alexei Kosygin.

A third theory was that he wanted presidential post or perhaps Kosygin's job for a protege whom he hoped to groom for the succession.

Whatever the truth, there was no denying Brezhnev's present eupremacy. What is in doubt is whether he can manage history without, as Stalin and Khrushchev did, setting in motion events that outrun his control.