Transmission and reflection of the light in films with helical periodical structure and enormous anisotropy are studied. We found strong evidence that in MgF2 there is a range (window) of frequencies for the incident light where strong anisotropy takes place. It is shown that in helical periodical media (HPM) with large anisotropy, the circular dichroism in diffraction (selective) reflection region (DRR) decreases with the increasing of the parameter of anisotropy delta = (epsilon(1) - epsilon(2))/(epsilon(1) + epsilon(2)) (where epsilon(1) and epsilon(2) are the principal values of the local dielectric constant tensor) and vanishes in the limit delta >> 1. The linear dichroism has the reverse behavior: it is equal to zero in the limit delta << 1 and increases to the maximum value equal to one in the limit delta >> 1. The DRR's structures were also found at certain conditions for HPM calculated in the presence of dispersion for the dielectric permittivity.