Start points of a misfire determining interval in the cylinders of an engine are specified by counting Pos signals starting from the appearance of a Ref signal in a specific cylinder. The Pos signals output from the Ref signal in each cylinder to the start point of the misfire determining interval are also counted as RGPHS after engine startup, and a shift of the misfire determining interval is detected by comparing for example the sum total of RGPHS for all cylinders and the sum total on the immediately preceding occasion. Correction of the misfire determining interval by a learnt value is stopped according to this shift. Preferably, correction of the misfire determining interval by the learnt value is restarted after making all misfire determining intervals the same by correcting for the shift.