  In the article we give some estimations of the {\L}ojasiewicz exponent of
nondegenerate surface singularities in terms of their Newton diagrams. We also
give an exact formula for the {\L}ojasiewicz exponent of such singularities in
some special cases. The results are stronger than Fukui inequality [8]. It is
also a multidimensional generalization of the Lenarcik theorem [13].
