<p><?tk 4?>The problem of recovering the relaxation time spectrum from discrete-time relaxation modulus measurement data is considered using the Post-Widder inversion formula and based on double-logarithmic-series-power model of the relaxation modulus. Using the specific properties of this relaxation modulus model, the product of the arbitrarily high power of time and the same order derivative of the relaxation modulus, which is the basis for the Post-Widder inversion rule, was expressed by analytical formula given by the series of recurrence-type, defined by the modulus model and triple-indexed integer coefficients introduced by simple recurrence equations. As a result, a new sequence of the Post-Widder approximations of the relaxation time spectrum was derived, given by recursive-type analytical formula. Two-stage identification scheme is presented for the relaxation spectrum model determination. In the first stage, the optimal double-logarithmic-series-power model is determined using Tikhonov-regularized linear least-squares method, applied to the log-transformed model and the relaxation modulus measurement data. Then, in the second identification stage, the calculation of the relaxation spectrum model is based on the recursive analytical formula of the Post-Widder approximation of arbitrarily high order. Finally, an example of the identification of the Baumgaertel-Schausberger-Winter spectrum is presented, which is characterized by a very wide range of relaxation times. It has been shown that the proposed method provides a very good approximation of the actual relaxation spectrum even for strong measurement noises.</p> Graphical abstract <p></p>