A new approach to investigations of ultra-high energy cosmic rays based on ground-level measurements of the spectra of local density of EAS muons at various zenith angles is considered. Basic features of local muon density phenomenology are illustrated using a semi-analytical model. It is shown that muon density spectra are sensitive to the spectrum slope and primary composition. Experimental data on muon bundles obtained with coordinate detector DECOR are compared with CORSIKA-based simulations. It is found that measurements of muon density spectra in inclined EAS allow the possibility to study characteristics of primary cosmic rays in a wide energy range from 10 15 to 10 19 eV.