But, in a state where insurance industry officials say four of the nation's six largest insurers refuse to go, Consumer First Insurance Co., of Clifton, N.J., and Rutgers Enhanced Insurance, a subsidiary of Rutgers Casualty of Cherry Hill, N.J., have begun writing business.

Consumer First opened for business last week. A small, start-up company, its business will be aimed at the urban market. Rutgers Enhanced began writing business on April 15 to cover higher risk drivers not covered by Rutgers Casualty, said Peter Hartt, spokesman for the New Jersey Department of Banking and Insurance.

While these insurers are opening their doors to new customers, talks are still going on between New Jersey Insurance Commissioner Holly C. Bakke and the state's major auto insurer, State Farm. The company is planning to leave the state's auto insurance line because, they say, the company cannot turn a profit.

Refusing to characterize the discussions, Mr. Hartt said the two sides are talking. Under state law, the department is required to give some notice to a company on their plan to leave the state within a time period, which, for State Farm, would be sometime in July.

Whatever the decision, Mr. Hartt said, if State Farm does finalize plans to leave, the company's leaving would be a gradual departure. The plan would allow customers time to obtain new coverage and not overburden existing insurers.

The New Jersey Coalition for Auto Insurance Competition, a coalition of industry and agent association interests, has pointed to State Farm and other insurers who have left New Jersey as evidence that the state's auto insurance laws are too restrictive.

John K. Tiene, chief administrative officer and vice president, public relations, the Insurance Council of New Jersey, which is a member of the group, said there is a process going on now to educate residents and legislators about the state of the insurance market in New Jersey.

He said no legislative proposals have been introduced yet to change the state's current laws, but there is a serious need to "create predictability" in the state's insurance market.

"We are not at that point yet to see legislation introduced," Mr. Tiene said. "At this point we are looking to help people understand the concept [of insurance competition] and to understand how to get there."

Among some of the issues considered "onerous" by insurers is a slow approval process for rate increases, a 6 percent cap on profits, and the "take all comers" law that mandates insurers take all applicants regardless of risk.