Using the Gleeble 1500, incremental and continuous hot compression tests, simulating hot rolling, were performed on C-Mn, Nb-T1 and Nb steels with test temperatures varying between 875 and 1100-degrees-C and strain rates between 0.5 and 20 s-1. Four models are proposed. The stress peak model allows the prediction of continuous stress-strain curves from incremental curves and vice versa through the use of stress restoration index K. Variation in K for Nb-T1, C-Mn and Nb steels at strain rates of 3, 12 and 20 s-1 was found to be negligible. The predicted stress strain curve corresponds to experimental stress strain curve at same temperature and strain rate. The strain history model predicts continuous strain-time curves from incremental stress-strain curves using 'constant' 'negative strain' restoration index. At 950-degrees-C, with holding time 2 s and strain rate 12 s-1, strain time decay curves obtained for C-Mn, Nb and Nb-T1 steels were epsilon = 1.5e-0.5t, epsilon = 1.2e-0.36t and epsilon = e-0.3t, respectively. The creep model analysis relates creep strain rate to the testing strain rate. For Nb steel at 875-degrees-C, and test strain rate of 12 s-1, epsilon(creep) was found to be 9.5 s-1. The stress history model predicts continuous stress-time curves from incremental stress-time curves. Stress decay curve for C-Mn steel at 1100-degrees-C and epsilon = 3s-1 was found to be sigma = 181e-0.04t. Hot rolling characteristics of steels can be accurately predicted using hot compression tests and proposed models.