We present theoretical results for the magnetic properties of modeled two-dimensional (2-D) Langmuir-Blodgett films consisting of different types of stable organic pi-monoradicals. Their energy spectra and magnetic characteristics are investigated using the many-body band theory of magnetism in pi-electron approximation. The main factors which determine the magnitude and character of the magnetic interaction in the 2-D molecular arrangements are thoroughly studied. Semiempirical electronic structure calculations have been also carried out for molecular clusters to gain further insight into their magnetic properties. The proposed models for LB films are potential candidates for new 2-D ferromagnetic materials which are characterized by a substantial increase of the critical temperatures up to 250 K in comparison to only about 5 K for the now existing magnetic LB films based on organometallic systems.