A method for the study of the steady-state nonlocal electron kinetics in radially and axially inhomogeneous cylindrical plasmas is presented. The method is based on the solution of the relevant space-dependent kinetic equation for the electron velocity distribution using the two-term expansion. A three-dimensional initial boundary value problem for the isotropic distribution component with the total energy as the evolution variable of the kinetic problem has to be treated. The technique is applied to analyze the electron kinetics in a cylindrical DC column plasma under impart of a space-independent axial field and a radially increasing radial field. Particularly, the spatial relaxation of the electron gas in axial direction in response to a disturbance of the axial homogeneity is investigated. A detailed analysis of the spatia(ly resolved energy balance is given. Considerable modification of the results with respect to those obtained by earlier studies of axially homogeneous DC column plasmas, as well as of relaxation processes in one spatial dimension, has been found.