The electronic structure of the praseodymium monopnictides and monochalcogenides is studied using the self-interaction corrected (SIC) local spin density (LSD) approximation. This method allows for a description of the Pr ions with some f electrons localized in atomic like orbitals, while other f degrees of freedom are forming hybridized bands. In this way different valency configurations of the Pr ion may be compared. The ground state configuration is obtained from the global energy minimum. With trivalent Pr ions, corresponding to two localized f electrons per Pr ion, the experimental lattice constants and bulk moduli of all these compounds are well reproduced. In contrast, the conventional LSD band treatment of the Pr pnictides and chalcogenides yields too small lattice constants. With applied pressure, the Pr monopnictides and monochalcogenides undergo simple B1 to B2 structural transitions which are well reproduced by the present theory without destabilization of the localized f 2 shells.