Several authors have suggested that, instead of being unit root processes, some macro variables may actually be stationary around nonlinear deterministic trends (Perron, 1989, 1990, Bierens, 1997). This paper investigates this for four variables in a standard money demand specification, using Canadian data. Evidence is first presented that the null of unit root with drift (constant, linear, or nonlinear) can be rejected in favor of nonlinear trend stationarity for the variables. Then, Bierens' (2000) nonlinear co-trending test finds two common nonlinear trends among the variables. The trends are consistent with a standard money demand relationship. All unit root and co-trending test conclusions are based on size and power results from Monte Carlo simulations as well as on asymptotic critical values. The paper concludes with a discussion of how the observed nonlinear trending and co-trending might arise in a theoretical model, and with implications for further empirical tests.