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A speech signal captured by a distant microphone is generally smeared by reverberation, which severely degrades automatic speech recognition (ASR) performance. One way to solve this problem is to dereverberate the observed signal prior to ASR. In this paper, a room impulse response is assumed to consist of three parts: a direct-path response, early reflections and late reverberations. Since late reverberations are known to be a major cause of ASR performance degradation, this paper focuses on dealing with the effect of late reverberations. The proposed method first estimates the late reverberations using long-term multi-step linear prediction, and then reduces the late reverberation effect by employing spectral subtraction. The algorithm provided good dereverberation with training data corresponding to the duration of one speech utterance, in our case, less than 6 s. This paper describes the proposed framework for both single-channel and multichannel scenarios. Experimental results showed substantial improvements in ASR performance with real recordings under severe reverberant conditions.