  This is a continuation of the authors' previous work [math.AT/9910001] on
classification of equivariant complex vector bundles over a circle. In this
paper we classify equivariant real vector bundles over a circle with a compact
Lie group action, by characterizing the fiber representations of them, and by
using the result of the complex case. We also treat the triviality of them. The
basic phenomenon is similar to the complex case but more complicated here.
