We explore the implementation of generalized Sturmian functions for the study of ionization of molecules by photon or electron impact. A first part is devoted to finding a good enough description of the molecular model scattering potential and imposing accurate asymptotic boundary conditions to the molecular continuum wave functions. A second part deals with the calculation, within a generalized Sturmian approach, of single ionization cross sections for small molecules such as CH4, H2O and NH3. Issues related to the random molecular orientation are addressed.