  We discuss self-similar solutions to $O(4)$ textures in Minkowski space and
in flat Friedmann-Robertson-Walker backgrounds. We show that in the Minkowski
case there exist no solutions with winding number greater than unity. However,
we find besides the known solution with unit winding number also previously
unknown solutions corresponding to winding number less than one. The validity
of the non-linear sigma model approximation is discussed. We point out that no
spherically symmetric exactly self-similar solutions exist for radiation or
matter dominated FRW cosmologies, but we find a way to relax the assumptions of
self-similarity that give us approximative solutions valid on intermediate
scales.
