This article considers tests for parameter stability over time in general econometric models, possibly nonlinear-in-variables. Existing test statistics are commonly not symptotically pivotal under non-standard conditions. In such cases, the external bootstrap tests proposed in this paper are appealing from a practical view-point. We propose to use bootstrap versions of the asymptotic critical values based on a first order asymptotic expansion of the test statistics under the null hypothesis, which consists of a linear transformation of the unobserved “innovations” partial sum process. The nature of these transformations under non-standard conditions is discussed for the main testing principles. Also, we investigate the small sample performance of the proposed bootstrap tests by means of a small Monte Carlo experiment.