In this paper, we describe a novel approach to speech recognition by directly modeling the statistical characteristics of the speech waveforms. This approach allows us to remove the need for using speech preprocessors, which conventionally serve a role of converting speech waveforms into frame-based speech data subject to a subsequent modeling process. Central to our method is the representation of the speech waveforms as the output of a time-varying filter excited by a Gaussian source time-varying in its power. In order to formulate a speech recognition algorithm based on this representation, the time variation in the characteristics of the filter and of the excitation source is described in a compact and parametric form of the Markov chain. We analyze in detail the comparative roles played by the filter modeling and by the source modeling in speech recognition performance. Based on the result of the analysis, we propose and evaluate a normalization procedure intended to remove the sensitivity of speech recognition accuracy to often uncontrollable speech power variations. Effectiveness of the pro- posed speech-waveform modeling approach is demonstrated in a speaker-dependent, discrete-utterance speech recognition task involving 18 highly confusable stop consonant-vowel syllables. The high accuracy obtained shows promising potentials of the proposed time-domain waveform modeling technique for speech recognition.