The problem of structural change justifiably attracts considerable attention in econometrics. A number of different paradigms have been adopted ranging from structural breaks which are sudden and rare to time-varying coefficient models which exhibit structural change more frequently and continuously. This paper is concerned with parametric econometric models whose coefficients change deterministically and smoothly over time. In particular we provide and discuss tests for the null hypothesis of no structural change versus the alternative hypothesis of smooth deterministic structural change. We provide asymptotic tests for this null hypothesis. However, the finite sample performance of these tests is not good as they overreject significantly. To address this problem we propose and justify bootstrap based tests. These tests perform well in an extensive Monte Carlo study.