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How to check if two samples are from the same distribution, when the variable is cyclic?

A simple answer for non-cyclic variable is the Kolmogorov-Smirnov test. What is the equivalent for cyclic variables? Is there other powerful similar tests specific for cyclic variables?

In my specific case I have two samples of an angle in $[0, 2\pi]$. The two distributions are nearly uniform, but not perfectly.

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    $\begingroup$ N..H. Kuiper and G.S. Watson proposed tests based on the empirical cdf. $\endgroup$ – Nick Cox May 24 '16 at 20:56
  • $\begingroup$ Ruggero: To my recollection Watson's 1961 paper deals with the one-sample case, but Watson's 1962 Biometrika paper (Goodness of fit tests on a circle, II) deals with the two-sample version of his test, which is what you're asking for here. Kuiper's paper - just having checked now - deals with both cases. $\endgroup$ – Glen_b May 24 '16 at 23:09

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