This paper provides exact (finite-sample) test critical values for carrying out tests of no cointegration versus some forms of nonlinear (threshold autoregressive) cointegration. The nonlinear models, which include threshold autoregressive and momentum threshold autoregressive behavior of deviations from long-run equilibrium, are easier to evaluate with the aid of the reported critical values. The results cover a variety of practical situations, with varying sample sizes, lag lengths, and number of time series.