Nonparametric tests for circular regression models (models where the response and/or the covariate are circular variables) are introduced and analysed in this work. Based on nonparametric smoothers for estimating regression curves, no-effect tests are first introduced. Nonparametric Analysis of Covariance (ANCOVA) models are also stated in the circular regression context, and testing tools for assessing equality and parallelism are presented. The finite sample performance of the proposed methods is analysed in a simulation study. Illustration with real data examples is also provided.