Abstract: A varying coefficient, nonlinear dynamic cascade model has been derived in this paper, thus, in fact, is the extension of a simple linear dynamic cascade model, obtained through process mechanism studies on a Purex process occurring in a sixteen stage extractor with a countercurrent of first recycling. A variable step width floating-point linearization algorithm for solving the nonlinear dynamic cascade model is hereby proposed. Dynamic distribution of extracted materials in different stages and its variation with time disclosed. Comparison at experimental values with theoretical values in the sensitive stage, gives rather satisfactory conformity.