J-C. Douai Title: "Hasse Principle and Group Cohomology. In a recent article, Colliot-Thelene, Gille and Parimala have considered fields K of cohomological dimension 2, of geometric type, analogous to totally imaginary numbers fields. One standard example is the field C((x,y)) (local-local(ll)).From Borovoi's results related to our previous results, they compute the cohomology of K in degree one and two with coefficients in a semi-simple K-group. The aim of our talk is to extend their results to fields of cohom.dim.2 that are not of geometric type but that, as the fields (ll), satisfy to Hasse Principle. By Efrat, one example of such a field is given by an extension of PAC field of relative transcendence degree 1 . We show that is possible to calculate the non abelian cohomology in degree two with coefficients in a semi-simple K-group where K is such a field (the cohomology in degree one is calculated by Serre's conjecture about the fields of cohomological dimension 2). We show also, in the case where K is of transc.degree 1 over a PAC field that, if the group is semi-simple and direct factor of a K-rational variety, then its Shafarevitch's group is trivial, getting an analogous result to a Sansuc's result for the number fields. For the fields (ll), the analogous result was established by Borovoi-Kunyavskii.