The distance d(u, v\G) between the vertices u and v of a molecular graph G is the length of a shortest u, v-path. We consider a class of Wiener-type topological indices W-i(G), defined as the sum of the terms d(u, v\G)(lambda) over all pairs of vertices of G. Several special cases of W-lambda(G), namely for i = +1 (the original Wiener number) as well as for lambda = -2, - 1, +1/2, +2 and +3, were previously studied in the chemical literature, and found applications as molecular structure-descriptors. We establish a relation between Wlambda+1 and W-lambda, applicable for benzenoid molecules, phenylenes, chemical trees, and other types of molecular graphs. (C) 2003 Elsevier Science B.V. All rights reserved.