Progreso Mayor Omar Vela, his school board president brother and their father will all remain in jail another night.
Accused in a bribery scheme, the three appeared for a bond hearing before U.S. Magistrate Judge Dorina Ramos in McAllen on Tuesday morning.
Vela his brother Michael Vela and their father Jose Guadalupe Vela, Jr. all appeared to be wearing the same clothes they were arrested in last week.
Federal prosecutors filed a brief over the Labor Day holiday that still needs to be reviewed by Judge Ramos.
Court records remain sealed in the case but Judge Ramos postponed the bond hearing until 11 a.m. Wednesday morning.
Family members and supporters packed the courtroom but declined to comment while leaving the courthouse.