  The interest in rigid vector bundles (with respect to determinant preserving
deformations) stems from various sources. From a geometric point of view,
non-K\"ahler manifolds are of particular interest with respect to this problem.
In this article, a description of the various possible cases of rigid rank 2
bundles on non-K\"ahler surfaces is presented. The largest gap of knowledge is
for minimal class VII surfaces with $b_{2}(X)\ge 4$.
