[en] A linear adiabatic and non-adiabatic survey of pulsation periods (up to the fourth overtone) was performed in the parameter ranges relevant for double-mode RR Lyrae stars. It was shown that among the lowest order resonances between the frequencies of the normal modes the closest is the 2:1 resonance between the fundamental and third overtone. It is argued that proper inclusion of non-adiabaticity may further improve the situation for this resonance. However, there is a problem with satisfying simultaneously constrains imposed by observed periods and resonance condition. As a by-product of our survey it was shown, that systematic differences exist between the different pulsational codes, causing uncertainty of 10-20 percent in mass determination. 22 refs., 8 figs., 1 tab. (author)