In this talk, we consider a boundary-value problem with the nonlocal integral condition of the rst kind for the parabolic equation with a singularity and discuss the question of numerical approximation of the solution. First, we prove existence and uniqueness of the solution to the nonlocal problem in the appropriate weighted functional space using ideas of the apriori estimates approach. Then we describe the homotopy analysis method (HAM) and study its optional applications to the nonlocal parabolic problem. We derive nth order deformation equations and obtain HAM-approximations to the solution. Finally, we consider the application of the homotopy analysis method to boundary-value problems with nonlocal boundary conditions of other types.