WHO WILL control the Chicago city council?

That was the question that Illinois politicians and journalists were asking about last week's primary -- while Lyndon LaRouche's fringe candidates ran off with the Democratic nominations for lieutenant governor and secretary of state. Few were paying attention to these contests, or for that matter, to the contests for governor and U.S. senator. Instead attention was forcused on the roughneck battles between Mayor Harold Washington and Edward Vrdolyak. For three years the 29-21 Vrdolyak majority on the Board of Aldermen has kept Washington appointees out of office; charges and countercharges, allegations and imprecations have filled the air. The seven special aldermanic races ordered by a federal court threatened to overturn "the 29"; henc the close attention.

The suspense continues. There will be a runoff in one race next month, which the mayor's candidate is expected to win. The 26th ward race is in court, with Mr. Vrdolyak's Manuel Torres 20 votes ahead of the mayor's Luis Gutierrez. On the outcome of this race will likely depend control of the council. The question remains what import all this has beyond the Chicago equivalent of the Beltway. The Washington-Vrdolyak struggle is sometimes painted as a battle between black and white: the 1983 election divided the city on racial lines, as candidate Washington proclaimed "Now it's our turn" and his Republican opponents urged people to vote against him "before it's too late." But most of last week's seven aldermanic races were between or involved Hispanic candidates, and the lines were not drawn strictly on ethnic lines. The real issue between the two sides is, as usual in Chicago politics, jobs -- but far fewer jobs than in the past. The Vrdolyak 29 have blocked the mayor's appointments to park district and transit authority boards that control some patronage jobs. The mayor has always maintained that he stands for reform -- a claim that will be put to the test if his candidates win.

For years patronage was a kind of cement that smoothed over such conflicts; the Democratic organization held together and pacified the potentially mutinous and hostile masses of a giant, rapidly growing and changing city. Now all that is changing, even as the shouting grows shriller. Old ethnic groups have settled in and hostilities faded; immigrants' children got prosperous and moved to the suburbs; a federal court ruling prohibits hiring and firing for political reasons in the large majority of public jobs. Mayor Daley's unusual skills may have prolonged the system beyond its ordinary life. But he has been gone nearly 10 years now.

The Washington-Vrdolyak struggle will surely continue in 1987. It will give Chicago politics the appearance of a racial battle and the substance of a fight over patronage. But the stakes are growing smaller. Chicago machine politicians could once deliver votes in presidential elections; now they cannot beat Lyndon LaRouche's candidate in the race for lieutenant governor. Aficionados of Chicago politics like to see it as a harbinger of national things to come. It's more like the opposite: the last example of a politics you used to find in most cities and these days are seeing in fewer and fewer places.