This work is a contribution to the development of asymptotic preserving numerical schemes for kinetic equations. To understand the main idea, we consider a model A in which a small parameter is present and a model B which is a non-trivial limit of the model A when the parameter tends to 0. The problem consists in constructing numerical schemes preserving this limit, and which are consistent with both models A and B. This allows to consider different regimes where the small parameter changes the scale in different zones of the space domain and where the two models have to be considered to treat the phenomenon under consideration. This talk contains two parts. The first one is concerned with the development of numerical schemes for like Boltzmann kinetic equations, which are able to preserve the Euler limit as well as the compressible Navier-Stokes asymptotics (which is not a limit) near the hydrodynamical regime. Our strategy consists in rewriting the kinetic equation as a coupled system of kinetic part and macroscopic one, by using the micro-macro decomposition of the distribution function as a sum of its corresponding (Maxwellian) equilibrium distribution plus the deviation. The simulations are performed for the one-dimensional BGK model, and then extended for this model in higher velocity dimension. The second part is concerned with the construction of asymptotic preserving scheme in the diffusion limit for the Kac’s equation. This model is much simpler that the Boltzmann equation (it is one dimensional), but it has the same quadratic structure, while the models used in the previous part were only relaxation operators. However, contrary to the Boltzmann equation, the natural fluid limit of the Kac model is a non linear diffusion equation. We also construct in this part a deterministic velocity discretization for the collisional operator. Such discretization is based on a simple new formulation of the Kac operator. Several simulations are presented in order to illustrate the efficiency of our approach.