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The method of recursive least squares, which has been used extensively in the field of system identification will be developed for adaptive parametric spectral estimation of digital signals. The method will be applied for adaptive pulse estimation and deconvolution of seismic data. Unlike the Levinson-type deconvolution method, the adaptive least-squares method does not need to estimate a priori the autocorrelation function and it avoids the windowing problem of a time-limited signal. Because of the recursive nature of the method, it is suitable for adaptive estimation and removal of time-varying pulses, and it is computationally simple and suitable for implementation on small computers with less memory requirements. The method has been implemented on different simulated examples, and the results are given and discussed.