This paper considers cointegrating regressions with time varying coefficients. The coefficients are modeled as smooth functions evolving over time. It is shown that they can be estimated nonparametrically, using suitably modified series estimators. Presented is the efficient method of estimation, which relies on simple prefiltering of the data and preestimation of the model. The test for the adequacy of model specification is also developed. Our model and statistical methods are applied to analyze the U.S. automobile demand function.