The normal-mode spectrum of the linearized resistive magnetohydrodynamics (MHD) operator is determined numerically for an inhomogeneous plasma slab. The spectrum consists of fast and slow magnetosonic and Alfvén sub-spectra. The obtained Alfvén sub-spectrum consists of discrete resistive Alfvén modes and an 'ideal quasi-mode' that originates from a surface mode due to a sharp density transition layer in the plasma. The quasi-mode interacts with the resistive Alfvén modes when the width of the transition layer is modified. Eventually, when the transition layer spreads over a substantial part of the plasma, the quasi-mode even loses its global or 'collective' behaviour and gradually transforms into an ordinary resistive Alfvén mode. In other words, it joins the resistive Alfvén sub-spectrum. Avoided crossings occur during the interactions of the ideal quasi-mode and the resistive spectrum.