A self-diagnosing apparatus for determining whether a failure in any one of inner cylinder pressure responsive sensors occurs, said inner cylinder pressure responsive sensors being disposed on respective engine cylinders so as to detect pressures within the respective engine cylinders for the respective engine cylinders and output inner cylinder pressure responsive signals indicative thereof, wherein said first average value is expressed as BGIMEP.sub.i (n)=BGIMEP.sub.i (n--1).(1-.alpha.)+IMEP.sub.i (n)..alpha., wherein IMEP.sub.i (n) denotes the integrated value derived by said integrating means at the time of (n), i denotes a cylinder number, (n-1) denotes the previous value of the presently derived average value (n), and .alpha. denotes a first weight coefficient and wherein said second average value is expressed as TBGIMP.sub.(n) =TBGIMP.sub.(n-1).(1-.beta.)+IMEP.sub.(n)..beta., wherein .beta. denotes a second weight coefficient.