Various electrooptic and magnetooptic effects enable the electric and magnetic field control of the holographic information recording. They can become significant if the frequency of light irradiation is close enough to the absorption line of a material. In this paper, these effects are theoretically considered, and the influence of applied external electric (up to 17 kV/cm) as well as magnetic field (0.15T) is experimentally studied on the transmission holographic grating recording in azobenzene-based molecular films at 632.8 and 532 nm. Recording beam polarizations were s-s, p-p, L-L and L-R . Self-diffraction efficiency (SDE) exposure time dependences were measured with and without the applied fields, and maximum SDE values as well as recording energies corresponding to 0.017% SDE were determined. No effect of electric field was found within the measurement accuracy (1-5%). Some trend to recording efficiency increase by magnetic field was observed. This result is in the agreement with the theoretical analysis. Unfortunately, these results are within experimental errors (usually 15-24%).