  The classification problem for principal fibre bundles over two-dimensional
CW-complexes is considered. Using the Postnikov factorization for the base
space of a universal bundle a Puppe sequence that gives an implicit solution
for the classification problem is constructed. In cases, when the structure
group $G$ is path-connected or $\pi_{1}(G) = 0$, the classification can be
given in terms of cohomology groups.
