Recently, we have developed equipment which can be used for both cyclotron resonance ͑CR͒ and electron spin resonance ͑ESR͒ measurements for studying f-electron systems. Using this equipment and preparing high-quality single crystals with a residual resistivity ratio of about 500, we have successfully observed CR signals in rare-earth monopnictides RX ͑R =La,Ce,Pr,Gd,X =Sb,Bi͒. The purpose of this paper is to describe the development of our measurement system in detail and to reexamine our recent results of CR measurements on the single crystals of RX. And then, we discuss the origin of mass enhancement in this system by comparing the case of a strongly correlated f-electron system CeSb with the case of a nonmagnetic simple semimetal LaSb. The CR measurements have been performed in the temperature range from 1.4 K to 40 K and in the frequency range from 50 to 190 GHz. We have observed CR signals in LaSb, LaBi, CeSb, PrSb, and GdSb. The cyclotron effective masses m CR * determined by the CR measurements are compared with the masses m QO * estimated by measurements of quantum oscillations and the masses m BC * deduced from band structure calculations. The determined m CR * of LaSb, LaBi, and GdSb is in the range of ͑0.17-0.65͒m 0 . These values are reasonably consistent with the values of m QO * and m BC * . This fact shows that both m CR * and m QO * mainly depend on the band structure if the interaction between conduction electrons and f electrons is negligible. On the other hand, in the case of a strongly correlated f-electron system CeSb, m CR * is in the range of ͑0.26-1.5͒m 0 . These values are much larger than those of m BC * . This finding shows that m CR * , as well as m QO * , is considerably enhanced in CeSb. Our results indicate that the interband interaction is important for the mass enhancement of m CR * in CeSb.