The effect of the cross-link density on the molecular dynamics of copolymers composed of vinylpyrrolidone (VP) and butyl acrylate (BA) was studied using differential scanning calorimetry (DSC) and dielectric relaxation spectroscopy (DRS). A single glass transition was detected by DSC measurements. The dielectric spectra exhibit conductive processes and three dipolar relaxations labeled as α, β and γ in the decreasing order of temperatures. The cross-linker content affects both α and β processes, but the fastest γ process is relatively unaffected. An increase of cross-linking produces a typical effect on the α process dynamics: (i) the glass transition temperature is increased, (ii) the dispersion is broadened, (iii) its strength is decreased and (iv) the relaxation times are increased. However, the β process, which possesses typical features of a pure Johari-Goldstein relaxation, unexpectedly loses the intermolecular character for the highest cross-linker content.