Abstract: Let ((n_k)) be an increasing sequence of positive integers. For most x in (0,1) the pseudo random sequence ((n_k.x mod 1)) behaves like a random numbers sequence. If we endow (0,1) with Lebesgue measure ((n_k.x mod1)) can be interpreted as a sequence of dependent random variables having uniform distribution over the unit interval. Starting with H. Weyl who proved what probabilists would now call a Glivenko Cantelli theorem, continuing with Salem and Zygmund who proved a central limit theorem for the cosines of these sequences, and Erdoes and Gal who proved a law of the iterated logarithm, it has been shown in many cases that these sequences share many properties of independent identically distributed random variables. In this talk I will report on some recent results (jointly with I. Berkes and R. Tichy) on pair correlations of such sequences, if ((n_k)) satisfies a Hadamard gap condition, and on generalizations (jointly with R.Tichy) of some recent results by Mauduit and Sarkoezy on distribution measures of such sequences.