The theory of resistive dissipation of linear compressible modes in a nonuniform plasma is presented in a unified way, following a normal mode approach. The familiar modes of a homogeneous ideal plasma are shown to be substantially modified by the presence of the resistivity and nonuniformity. It is then argued that the most suitable criterion for mode identification is based on the asymptotic properties of the solutions. The modes are then classified as ideal or resistive according to the asymptotic absence or presence of the resistivity. After a brief summary of the results from previous articles, made for the sake of completeness, the article concentrates on the new results concerning the compressible ideal solutions, the only ones that exhibit a resonant behavior. The properties of the solutions are examined by treating an explicit example of a nonhomogeneous situation. It is shown that the nature of the modes varies in the direction of nonuniformity, being essentially a fast mode in the asymptotic region, a slow mode in the vicinity of the so-called cusp resonance, and an Alfvenic mode near the Alfvenic resonance point.