  In the present paper we study the structure of the cut locus of a Randers
rotational 2-sphere of revolution $(M, F = \alpha+\beta)$. We show that in the
case when the Gaussian curvature of the Randers surface is monotone along a
meridian, the cut locus of a point $q\in M$ is a point on a subarc of the
opposite half bending meridian or of the antipodal parallel (Theorem 1.1). More
generally, in the case when the Gaussian curvature is not monotone along the
meridian, but the cut locus of a point $q$ on the equator is a subarc of the
same equator, the cut locus of any point $\widetilde q\in M$ different from
poles is a subarc of the antipodal parallel (Theorem 1.2). Some examples are
also given at the last section and some differences with the Riemannian case
are pointed out.
