A diagnostic method is presented and tested with four-cylinder compression and spark ignition engines for the diagnosis of cylinder power faults. The method uses the two-sided directional power spectra of complex-valued engine vibration signals. As the spectral estimators, the Autoregressive and Maximum Likelihood methods are used, and then the multi-layer neural network is employed for recognizing the pattern of spectra. Experimental results show that the use of directional power spectra results in much higher success rate for identifying misfired cylinder than the use of conventional one-sided power spectra.