  This paper focuses on the problem of testing the null hypothesis that the
regression functions of several populations are equal under a general
nonparametric homoscedastic regression model. It is well known that linear
kernel regression estimators are sensitive to atypical responses. These
distorted estimates will influence the test statistic constructed from them so
the conclusions obtained when testing equality of several regression functions
may also be affected. In recent years, the use of testing procedures based on
empirical characteristic functions has shown good practical properties. For
that reason, to provide more reliable inferences, we construct a test statistic
that combines characteristic functions and residuals obtained from a robust
smoother under the null hypothesis. The asymptotic distribution of the test
statistic is studied under the null hypothesis and under root$-n$ contiguous
alternatives. A Monte Carlo study is performed to compare the finite sample
behaviour of the proposed test with the classical one obtained using local
averages. The reported numerical experiments show the advantage of the proposed
methodology over the one based on Nadaraya-Watson estimators for finite
samples. An illustration to a real data set is also provided and enables to
investigate the sensitivity of the $p-$value to the bandwidth selection.
