LAPD Assistant Chief George Gascon said the estimates are based on street intelligence and what he described as a well-organized campaign involving radio stations, churches and community groups. Police do not expect trouble, he added.

Demonstrations are planned for downtown at noon and Mid-Wilshire at 4 p.m. Gascon said the LAPD is gearing up to deal with hundreds of thousands of demonstrators at each.

Los Angeles Mayor Antonio Villaraigosa, Cardinal Roger Mahony and others have encouraged protesters to attend the late-afternoon march from MacArthur Park down Wilshire Boulevard to La Brea Avenue, prompting authorities to say that crowd might be the larger of the two.

Officials in Santa Ana, Huntington Park, Oxnard, Riverside, Pomona and San Diego said they expect smaller but boisterous protests.

Police in Chicago, meanwhile, estimated that as many as 500,000 could take to the streets in that city, while Seattle officials and protest organizers said they expect anywhere from 10,000 to 50,000 marchers.

Officials acknowledged that it is difficult to predict the size of any protest crowd, noting that at a march last month, the LAPD had expected far fewer protesters than the estimated 500,000 people who showed up outside Los Angeles City Hall.

But if the LAPD's estimates prove correct, Monday's marches would approach the scope of that event — one of the largest protests in Los Angeles' history. Officials said Monday's demonstrations could prove more disruptive, however, because they will occur on a weekday and they include a call for people to boycott school and work and refrain from shopping.

Some small-business owners say they plan to close down Monday, either to support the marchers or because they think it would be difficult to do business.

State and local school officials urged students to stay in classes, and transportation officials planned street closures and bus route detours.

"We want students to exercise free speech, but not at the expense of their education," said state Supt. of Public Instruction Jack O'Connell. "If students need to protest, they should feel free to do so after school."

The LAPD is coordinating an action plan with the Sheriff's Department, transportation agencies, the school district and other law enforcement. Officials said they also have been in contact with organizers in hopes of minimizing any conflicts and making sure the demonstrations run smoothly.

"We feel very confident at this point about the way the demonstrators have been conducting themselves, and we don't anticipate any problems," Gascon said. "We want to protect the demonstrators' 1st Amendment rights as well as the property rights and the rights of everyone else in the community."

Authorities voiced concern that because the protest falls on May Day, revolutionary groups and anarchists who have given police trouble in the past might join the marchers.

"We are not sure what they will add to the mix," said LAPD Capt. Andy Smith of the Central Division.

The noon march in Los Angeles is scheduled to begin at Olympic Boulevard and Broadway and proceed north toward City Hall. It is organized by the March 25 Coalition, which has called for a boycott of work, school and consumer activity. Leaders say the goal is to demonstrate the vital role of immigrants in the economy.

The second march is scheduled to begin at MacArthur Park and head west on Wilshire Boulevard toward La Brea. Organizers include the Archdiocese of Los Angeles and labor and civic groups. They say they want to give people who cannot take the day off work a way to participate in the fight for immigrant rights, and have urged students not to miss school.

LAPD officials said they have heard about a possible third demonstration being organized for Monday night in downtown, but did not know how big it might be.

It is unclear how businesses will be affected by the protests. Most larger shops and companies appear to be planning regular operations Monday. But local businesses with large numbers of immigrant workers, as well as those owned by immigrants and establishments along protest routes, could face substantial disruptions.

Some restaurants, grocery stores, garment factories, farmers, meat packers, gardeners and truckers say they plan to suspend some or all operations. Households may not get their usual gardening or housecleaning services, while some commercial establishments may not receive expected deliveries. Some workers who plan to demonstrate have already cleared their absences with their employers, while others plan to work from home to avoid traffic problems.