In this work the problem of determining the dependencies on conversion of the initiation rate (R-i), the propagation (k(p)), termination (k(t)), and transfer to monomer (k(tr)) kinetic constants in the thermally initiated free-radical polymerization of styrene is addressed. A 2 nonlinear observability analysis establishes that the parameter groupings R-i, kappa = k(t)/k(p)(2), and C-m = k(tr)/k(p) dependencies on conversion can be determined on the basis of the species conservation balances in conjunction with conversion and (number- and weight-) average molecular weight experimental measurements, without making any a priori kinetic modeling assumption. Then, the differential estimation technique associated with the observability property is applied to previously reported experimental runs at 100, 120, 170, and 200degreesC, yielding the following results: (1) for the two lower temperature runs, R-i exhibits a nearly quadratic dependency on monomer concentration, and for the higher temperature the overall dependency is about cubic or quartic, and this behavior differs from that of the standard cubic-dependency model; (2) kappa shows an exponential-like decay with conversion that agrees with previous reports, and (3) C-m exhibits a quadratic-like increase with conversion that disagrees with the linear decay assumed before. (C) 2004 American Institute of Chemical Engineers.