The nonlinear step-growth copolymerization of a mixture of low-and high-molecular-weight diols, and a low-molecular-weight diisocyanate is addressed using a kinetic-probabilistic model. The kinetic model allows for the calculation of the concentrations of all species. Different reactivities for isocyanate functional groups located in different positions of the monomer and polymer molecules, as well as the hydroxyl functional groups of different molecules, are allowed. A recursive probabilistic model is used to calculate the number-and weight-average molecular masses. Allophanate and biuret ramification reactions, as well as gelation formation due to cross-linking, are considered in the model. The model is validated for the reaction of methyl diisocyanate (MDI) with a mixture of a polyester and 1,4-butanediol. Agreement between the model predictions and experimental data from the literature on diol conversion, weight-average molecular weight, and reaction mixture viscosity is satisfactory.