We present optical and infrared broad-band images, radio maps, and optical spectroscopy for the nuclear region of a sample of nearby galaxies. The galaxies have been drawn from a complete volume-limited sample for which we have already presented X-ray imaging. We modelled the stellar component of the spectroscopic observations to determine the star formation history of our targets. Diagnostic diagrams were used to classify the emission-line spectra and determine the ionizing mechanism driving the nuclear regions. All those sources classified as active galactic nuclei present small Eddington ratios (~10^-3^-10^-6^), implying a very slow growth rate of their black holes. We finally investigate the relative numbers of active and normal nuclei as a function of host galaxy luminosity and find that the fraction of active galaxies slowly rises as a function of host absolute magnitude in the MB~-12 to -22 range.