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The Keller Segel (KS) model for chemotaxis is a twodimensional system of parabolic or elliptic PDEs. Motivated by the study of the fully parabolic model using probabilistic methods, we give rise to a non linear SDE of McKeanVlasov type with a highly non standard and singular interaction. Indeed, the drift of the equation involves all the past of one dimensional time marginal distributions of the process in a singular way. In terms of approximations by particle systems, an interesting and, to the best of our knowledge, new and challenging difficulty arises: at each time each particle interacts with all the past of the other ones by means of a highly singular spacetime kernel. In this talk, we will analyse the above mentioned McKeanVlasov SDE and the associated particle system in order to exhibit new wellposedness results for the fully parabolic KS model in the case of $d=1$ and $d=2$. This is a joint work with D.Talay (Inria) and JF. Jabir (HSE, Moscow).