An implication of optimizing theory is that demand functions are homogeneous of degree zero in prices and nominal income. Evidence based on estimations of demand systems has repeatedly found this restriction to be rejected by the data. However, the hypothesis is often formulated in terms of regressors that are non-stationary. This paper re-examines the evidence for homogeneity in light of recent developments in time-series econometrics with special emphasis on the treatment of trends. We find the demand system to be stochastically but not deterministically cointegrated. Using techniques developed for estimating cointegrating vectors in the presence of deterministic trends, we re-estimate the demand system and find that homogeneity holds in many cases.