We have studied the ability of two one-dimensional (1-D) time-stepping models, both based on the concept of magnetic viscosity, to reproduce dynamic loops and losses in grain-oriented (GO) electrical steels under arbitrary magnetization regimes. We found that GO steels (0.3 mm thick) can be modeled quite accurately at magnetizing frequencies up to 200 Hz by a thin sheet representation, which is applied to a bulk material. At higher frequencies, acceptable results can be obtained through a finite-difference solver of a 1-D penetration equation whose applicability to GO steels can be explained in terms of domain wall bowing. Because of the inertial effect introduced by the magnetic viscosity, the average error in the loss prediction is reduced from 40% for the conventional classical method to 5% for the methods we studied. We demonstrated the accuracy of the models using two GO steels whose losses and B-H characteristics were measured by computer-controlled Epstein and single-sheet testers.