We study the effect of simultaneous excitation of the space charge and conductivity running gratings in photorefractive crystals. For the realization of such regime we illuminate the crystal by the interference pattern oscillating with frequency ω. The combination of external dc and ac (with frequency Ω) voltages is applied to the crystal as well. If the frequencies of the phase modulation and ac field are equal to the eigenfrequency of the conductivity grating oscillation (high-frequency branch of the space charge oscillation) ω,Ω=ωpc, and their difference is equal to the eigenfrequency of the space charge grating oscillation (low-frequency branch) |ω-Ω|=ωsc, then the former grating oscillation effectively interacts with the ac component of applied field giving rise to the latter one. The experiments are performed in the photorefractive sillenite crystals (Bi12SiO20, Bi12TiO20) using both the diffraction and non-steady-state photo-EMF techniques. The dependencies of the detected signal amplitudes on the difference frequency ω-Ω (for fixed Ω) and dependencies of the detected signal amplitudes on the frequency of phase modulation ω (for fixed ω-Ω) are measured. They demonstrate the excitation of both the low and high-frequency eigenmodes of the space charge oscillation and provide estimations of material parameters, namely, the mobility of photoelectrons: μ=(1.1-1.4)×10-2 cm2/Vs (Bi12SiO20, λ=532 nm, T=296-298 K), μ=1.5×10-2 cm2/Vs (Bi12SiO20, λ=442 nm, T=293 K), and μ=3.1×10-3 cm2/Vs (Bi12TiO20, λ=532 nm, T=293 K). The application of the developed techniques for the characterization of widegap semiconductors and for the detection of optical phase-modulated signals is discussed.