Abstract: A nonlinear dynamic cascade model with varying coefficients has becn derivcd for a sixteen-stage countercurrent extractor representing the first cycle of a Purex process. This actually is the result of further scrutinizing of the process mechanism and following-up of a simple linear dynamic cascade model formerly developed. A variable step length floating-point linearization algorithm for solving the nonlinear dynamic cascade model is proposed. The dynamic distribution of extracted materials in different stages and their variation with time are disclosed. Experimental data seem to conform quite satisfactorily with theoretical values obtained from the sensitive stage theory.