Change-point tests are meant to detect the point in time at which a sample of observations changes in the probability distribution from which they came. Suppose one has a set of independent vectors of measurements, observed in a time-ordered or space-ordered sequence. In our set-up, these observations are circular data and we are interested as to which point in time does the distribution change from having one mode to having more than one mode. In this work we model unimodality or bimodality with a mixture of two Circular Normal distributions, which admits both possibilities, albeit for different parameter values. Tests for detecting the change-point are derived using the generalized likelihood ratio method. We obtain simulated distributions and critical values for the appropriate test statistics in finite samples, as well as provide the asymptotic distributions, under some regularity conditions. We also tackle this problem from a Bayesian perspective.