We propose several new tests for monotonicity of regression functions based on different empirical processes of residuals and pseudo-residuals. The residuals are obtained from an unconstrained kernel regression estimator whereas the pseudo-residuals are obtained from an increasing regression estimator. Here, in particular, we consider a recently developed simple kernel-based estimator for increasing regression functions based on increasing rearrangements of unconstrained non-parametric estimators. The test statistics are estimated distance measures between the regression function and its increasing rearrangement. We discuss the asymptotic distributions, consistency and small sample performances of the tests.