  Conditions for the existence of repeatable light paths (RLPs) in the
shearfree normal cosmological models are investigated. It is found that in the
conformally nonflat models the only RLPs are radial null geodesics (in the
spherical case) and their analogues in the plane- and hyperbolically symmetric
cases. In the conformally flat Stephani models, there exist special
spherically-, plane- and hyperbolically symmetric subcases, in which all null
geodesics are RLPs. They are slightly more general than the Friedmann --
Lema\^{\i}tre -- Robertson -- Walker (FLRW) models of the corresponding
symmetries: their curvature index function $k(t)$ and the scale factor $R(t)$
are expressed through a single function of time. In addition to that, there
exist special cases of the Stephani solution in which some of the null
geodesics are RLPs. All these special cases are identified.
