The battle to bring an additional $5.6 billion into New York City public schools meets its next stumbling block today when attorneys for the Campaign for Fiscal Equity return to court to face off with the state.

Today’s hearing in Manhattan marks the latest iteration of an education funding battle that has been raging in the courts for more than a decade.

Governor Pataki and the lawyers for the campaign will each have 30 minutes, twice the normal allotted time, to present oral arguments to the Appellate Division of the state Supreme Court.

The equity lawyers are expected to continue fighting for extra education aid for New York City schoolchildren, who they contend are being denied the “sound basic education” they deserve under the state constitution.

Mr. Pataki’s representatives, who are appealing last year’s decision by state Supreme Court Justice Leland De-Grasse, are expected to argue that the courts should not decide how Albany should distribute education dollars in New York State.

The stakes are high in today’s court battle.

Last year, Justice DeGrasse appointed a panel of special referees to determine how much extra money would be required to level the playing field for New York City’s public schools.

Early last year, the referees recommended that New York City schools receive about $23 billion in extra education aid over the next five years.

They said the city should receive an additional $5.6 billion a year after a four-year phase-in period for operating expenses like buying books and paying teachers. They also called for an additional $9.2 billion over the next five years for capital costs like building new school facilities.

In late March, Justice DeGrasse ordered the state to adopt the panel’s recommendations immediately.

The governor quickly vowed to appeal the decision.

His appeal set off another round in a fight that, in recent years, seemed like it was heading toward a conclusion.

In June 2003, after 10 years of litigation and a seven-month trial, the Court of Appeals, the highest court in the state, ruled that New York City children were being denied the sound basic education they are guaranteed under the state constitution.

The Court of Appeals gave the state until July 30 to determine how much money would be needed to make sure every school would have adequate funds. Because the state did not meet the deadline, the court appointed three referees to accomplish the task.

The director of the Campaign for Fiscal Equity, Michael Rebell, yesterday called the case “a looming constitutional crisis.”

“We are going to ask this court to not only decide in our favor, we want a decision before January, before the next legislative session,” Mr. Rebell told The New York Sun. “We want to send a message that this is outrageous.”

A spokesman for Attorney General Eliot Spitzer, Brad Maione, declined to comment on today’s oral arguments.

Mayor Bloomberg and his schools chancellor, Joel Klein, have said that Albany should stop its appeal and grant New York City schools the court ordered funds. Earlier this year, the city’s top lawyer said Albany should deliver all the money, ensuring the city does not have to pay any portion of the extra costs. Lawmakers in Albany balked at the idea that the city shouldn’t split the bill.

Even though Albany is reluctant to put an end to the battle and send extra money to the city, the mayor and his Democratic opponent, Fernando Ferrer, have issued a number of proposals that rely on fiscal equity funds.

The mayor last week proposed more than doubling the number of children in early childhood programs. He said that plan would not be implemented until the city received almost $500 million in Campaign for Fiscal Equity funds.

Mr. Ferrer has criticized the mayor for not pushing hard enough in Albany to secure the money. He wants to implement a stock-transfer tax to raise money that the city would put toward paying 25% of the Campaign for Fiscal Equity bill. He says that plan would spur Albany to send down what he sees as its share of the package.