ELIZABETH, N.J. (AP)  -- Former Gov. James E. McGreevey and his estranged wife, having reached a deal on custody of their child, return to court Monday in a bid to settle other issues as they work to dissolve their marriage.

The child custody matters were settled after three days of closed-door negotiations at the Union County Courthouse, assisted by a judge who has been urging the nation's first openly gay governor and Dina Matos McGreevey to avoid a divorce trial.

While their lawyers said they hope for continued progress, Stephen P. Haller, lawyer for the former governor, acknowledges "the issues that remain are markedly different with different consequences."

The first to be tackled will be financial matters: alimony and child support, court spokeswoman Sandra Thaler-Gerber said. After that, they could tackle Matos McGreevey's claim of marriage fraud.

Her lawyer, John N. Post, said she was pleased with the custody arrangement for 6-year-old Jacqueline, which was not divulged since the record was sealed. "The judge was very, very helpful to both sides," Post said.

State Superior Court Judge Karen M. Cassidy took some testimony on the custody matter in a closed ninth-floor courtroom, but made no rulings, Thaler-Gerber said.

McGreevey declined to give specifics of the deal regarding the girl, but said, "She'll get a large amount of time to spend with her parents."

The courtroom also served as the base for negotiations. The two sides will continue their talks there, but testimony on financial issues would be open to the public, Thaler-Gerber said.

The former governor and his wife have been living apart nearly as long as they lived together.

They split in 2004, when McGreevey resigned during his first term after a nationally televised speech in which he acknowledged being "a gay American" and said he had an affair with a male staffer. The staffer has denied the affair and claims he was sexually harassed by McGreevey. The couple had been married for four years.

Since then, McGreevey began living at the home of his boyfriend and started studying for the Episcopal priesthood. Matos McGreevey worked as the executive director of a foundation for a Newark hospital before becoming a sometime analyst on cable television shows. Both wrote books and promoted them on Oprah Winfrey's television show.

Matos McGreevey claims she was duped into marriage by a closeted gay man who needed the cover of a wife to advance his political career. McGreevey contends she should have known he was gay and that the marriage was "a contrivance on both our parts."

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