In a parallel running control apparatus for inverter generator A having first, second and third inverters adapted convert alternating current outputted from windings wound around an alternator into direct/alternating current by driving switching elements, and CPUs to control turning ON/OFF of the switching elements, it is configured so that the generator A runs in parallel with at least one inverter generator B, which is configured to be same as the inverter generator A, to output a three-phase alternating current, and one of the CPU determines that the generator B was stopped when at least one of phase differences between a phase of an output from the first inverter and phases of outputs from the second and third inverters becomes greater than or equal to a predetermined value.