Abstract This paper analyses the effect of variations in the elimination rates of four elimination models. Three types of variations are studied: (1) a periodic change between two elimination rates; (2) changes between two elimination rates at random times; and (3), an elimination rate varying smoothly in time, generated by having the elimination rate vary exponentially with temperature and a sinusoidally varying temperature. The elimination process is described by four different models: (1) a single compartment; (2) two compartments in parallel; (3) two compartments in series; and (4) the Goldstein-Elwood model. It is shown that for all 12 cases, the solutions can be given the same form as with constant elimination rates through reinterpretation of the parameters. As a special case, the use of elimination methods to estimate respiration is discussed and a possible source of error is pointed out.