Many researches have invested their time in creating mathematical models that simulate the dynamic behavior of hydrodynamic journal bearings. In most of the cases a linear model for constant dynamic coefficients has been used, but recent comparisons between the theoretically and experimentally obtained coefficients have not shown the expected agreement. This research presents a linear model and a nonlinear model with constant coefficients, as a function of the displacement and velocity of the shaft center. The coefficients are determined using the minimum-square method to adjust the transient response of a journal-bearing system for different operating conditions. The adjustment is linear with a polynomial approximation function including third-grade terms. A comparison between these results and the results obtained with linear analytical methods, e.g. where perturbation about the equilibrium position, permits the establishment of a range where the bearing behaves linearly.