Abstract : The thesis is devoted to the homogenization of singular convection-diffusion equations and spectral problems with sign-changing density function. It consists of two parts. The first one contains both qualitative and asymptotic results for solutions of stationary and non-stationary convection-diffusion equations in bounded or unbounded domains. Among the studied problems are qualitative problem for a convection-diffusion equation in a semi-infinite cylinder, homogenization of convection-diffusion models in thin cylinders and asymptotic problems for non-stationary convection-diffusion equations with large convection term in bounded domains. The second part of the thesis deals with the homogenization of elliptic spectral problems with sign-changing density function. We show that the asymptotic behaviour of the spectrum depends crucially on whether the density average over the period is zero or not, and construct the asymptotics of the spectrum in both these cases.