A strange set of political bedfellows that includes the American Civil Liberties Union, a conservative Washington think tank, and Mayor Koch is telling the U.S. Supreme Court that the system New York uses to elect its state judges is unconstitutional.

They were among those who filed supporting briefs in New York State Board of Elections v. Lopez Torres, a case set for October that challenges New York’s singular system of conventions used to pick its trial judges.

The politics of the people and groups that filed the court briefs vary, but all said the convention system suffers from fatal flaws. In the other 49 states, trial judges either are appointed by elected officials or gain office by popular vote. In New York, delegates from the two main political parties gather at conventions, where they nominate the judge who will represent the party on the ballot. The judge who brought the case in 2004, Margarita Lopez Torres, charged that the nominating conventions are shams in which party bosses handpick candidates. Two lower federal courts have sided with Judge Lopez Torres, ruling that the system violates both the rights of voters and of challenger candidates.

A conservative Washington think tank, the Washington Legal Foundation, and a former Republican New York State senator and assistant U.S. attorney general under President George H.W. Bush, John Dunne, filed briefs against the judicial system. Two scholars, Norman Ornstein of American Enterprise Institute and Thomas Mann of the Brookings Institute, filed a brief jointly as well.

“They see a system which completely fences out the ordinary person, and I think that offends people just as much on the right side of the political agenda as on left side,” Judge Lopez Torres’s lead counsel, Frederick A.O. Schwarz Jr., said.

Mr. Koch, the Brooklyn district attorney, Charles Hynes, the city of New York, the New York State and City Bar Associations, and the Fund for Modern Courts also joined in the criticism of the convention system.

The Republican National Convention, the New York County Democratic Committee, the New York Republican State Committee, the Mid-Manhattan Branch of the NAACP, and the Metropolitan Black Bar Association had previously filed briefs supporting the convention system.

An attorney representing the New York State Board of Elections, Joseph Forstadt, discounted the supporting briefs.

“At the end of the day, all of the briefs turn on the question of what is the self-interest of the groups that are advancing their arguments,” Mr. Forstadt said.

An appointive system would be the least democratic solution of all, Mr. Forstadt said, and that is what the bar associations supporting Judge Lopez Torres aim to install, he added.

If the Supreme Court does not overturn the lower courts’ decision, the state Legislature will have to adopt a new method of selecting trial court judges.