When a shift routine is not being executed in an automatic transmission and a difference between an actual turbine speed and a calculated synchronous speed is equal to, or greater than, a preset value .alpha., a difference .DELTA.NT between an estimated turbine speed and the actual speed when the automatic transmission is in a neutral state is calculated. When .DELTA.NT is equal to, or less than, a preset value .beta., it is determined that a failure related to the neutral state of the automatic transmission has occurred. Also, when .DELTA.NT is greater than a preset value .beta., it is determined that a failure related to slipping of a frictional engaging element has occurred.