A connected subgraph of a benzenoid system is said to be a generalized benzenoid system of type T

denoted by TGB

if it has no vertex of valency one and every interior face of it is bounded by a hexagon. In this paper

we generalize the concept of a canonical P-V path on the boundary of a benzenoid system to that of a TGB. and prove that a TGB H has Kekule structures if and only if the subgraph obtained from H by deleting a canonical P-V path of H has Kekule structures

Furthermore

it is also proved that there are at least two canonical P-V paths on the boundary of a TGB. By the above results

a simple and efficient algorithm

called the canonical P -V path elimination

is founded for determining whether or not a given TGB H has Kekule structures. If H is Kekulean

the algorithm can find a Kekule structre of H.