The class of recurrent novae (RN) with thermonuclear runaways contains only three systems (T Pyx, U Sco, and V394 CrA), for which no orbital periods are known. This paper presents a series of photometric observations where the orbital periods for all three systems are discovered. T Pyx is found to have sinusoidal modulation with an amplitude of 0.08 mag and a period of 2.3783 h (with a possible alias of 2.6403 h). U Sco is found to be an eclipsing system with an eclipse amplitude of roughly 1.5 mag and an orbital period of 1.2344 days. V394 CrA is found to have sinusoidal modulation with an amplitude of 0.5 mag and a period of 0.7577 days. Thus two out of three RN with thermonuclear runaways (or five out of six for all RN) have evolved companions.