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In this paper, two algorithms are proposed to identify linear, time-varying (LTV) systems and model nonstationary signals. The first one is based on the time-varying cumulants (TVC); and the second one applies the time-varying sum-of-pseudo cumulants (TVSPC). We also have shown that if the output of the LTV system is corrupted by stationary/nonstationary noise with symmetric distribution, the time-varying coefficients of the system can be identified using the time-varying sum-of-cumulants and sum-of-pseudo cumulants algorithms. Some LTV system identification and nonstationary signal modeling examples are given, using the above algorithms.