The purpose of this paper is to provide practitioners with further insight into spurious damping forces that can be generated in nonlinear seismic response history analyses (RHA). The term 'spurious' is used to refer to damping forces that are not present in an elastic system and appear as nonlinearities develop: such damping forces are not necessarily intended and appear as a result of modifications in the structural properties as it yields or damages due to the seismic action. In this paper, two types of spurious damping forces are characterized. Each type has often been treated separately in the literature, but each has been qualified as 'spurious', somehow blurring their differences. Consequently, in an effort to clarify the consequences of choosing a particular viscous damping model for nonlinear RHA, this paper shows that damping models that avoid spurious damping forces of one type do not necessarily avoid damping forces of the other type.