Using measurements from the PAMELA and ARINA spectrometers onboard the RESURS DK-1 satellite, we have examined the 27-day intensity variations in galactic cosmic ray (GCR) proton fluxes in 2007-2008. The PAMELA and ARINA data allow for the first time a study of time profiles and the rigidity dependence of the 27-day variations observed directly in space in a wide rigidity range from ~300 MV to several GV. We find that the rigidity dependence of the amplitude of the 27-day GCR variations cannot be described by the same power law at both low and high energies. A flat interval occurs at rigidity R = <0.6-1.0> GV with a power law index $\gamma$ = - 0.13±0.44 for PAMELA, whereas for R ≥ 1 GV the power-law dependence is evident with index $\gamma$ = - 0.51±0.11. We have revisited the data of PAMELA and ARINA measurement and confirmed our previous results. We hope that the model of the GCR transport will explain the physical nature of the change in the shape of the rigidity spectrum of the 27-day GCR variation in the framework of a realistic picture of the CIR formation in the heliosphere.