The theory of resistive dissipation of linear compressible modes in a
nonuniform plasma is presented in a unified way, following a normal mo
de approach. The familiar modes of a homogeneous ideal plasma are show
n 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 solut
ions. 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 co
mpleteness, the article concentrates on the new results concerning the
compressible ideal solutions, the only ones that exhibit a resonant b
ehavior. The properties of the solutions are examined by treating an e
xplicit example of a nonhomogeneous situation. It is shown that the na
ture of the modes varies in the direction of nonuniformity, being esse
ntially a fast mode in the asymptotic region, a slow mode in the vicin
ity of the so-called cusp resonance, and an Alfvenic mode near the Alf
venic resonance point.