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Let G be a semisimple Lie group without compact factors, \Gamma be anirreducible lattice in G. In the first part of the article we give thenecessary and sufficient condition under which a sequence of translates ofprobability "horospherical measures" is convergent. And the limiting measure isalso determined when it is convergent (see Theorems 1 and 2 for the precisestatements). In the second part, two applications are presented. The first oneis of geometric nature and the second one gives an alternative way to count thenumber of rational points on a flag variety.

Translate of horospheres and counting problems