The modulating-function (MF) waveform analysis method has been generalized and applied to investigate the deep levels in semiconductors. The advantages of the MF method over other available methods-the method of moments, Fourier transform and least-squares-have been discussed and re-emphasized. As examples, the isothermal capacitance transients measured for GaAs (Si implanted) and Si (Au doped) have been analysed. The results for activation energy, capture cross section and density distribution are in general agreement with the experimental and calculated results published earlier.