In recent experiments[1] we have shown that the director fluctuations in nematic liquid crystal elastomers (LCE), as measured by dynamic light scattering, are a sensitive probe of the properties of LCE under strain, in particular with respect to the semisoft behavior. Semisoft elastic response originates in a symmetry breaking internal strain that was built into the material as a result of the procedure to obtain a monodomain sample. This strain is coupled to the nematic director, locking it into the orientation direction. It makes the relaxation rate of the director finite and essentially independent of the wave-vector. An applied external strain perpendicular to the orientation direction at a critical value, corresponding to the onset of the semisoft plateau, effectively cancels the anisotropy field acting on the director so that the relaxation rate at zero wave -vector goes to zero, reflecting the fact that in an ideal LCE the nematic director fluctuations are the Goldstone mode of the system. Our dynamic light scattering measurements of the relaxation rate of the nematic fluctuations as a function of strain an temperature are in complete accordance with the theory semisoft elasticity of Warner and Terentjev and combined with mechanical measurements allow us to determine all the parameters of the theory. Photosensitive LCE, doped with azobenzene derivatives undergoing trans to cis isomerization, are of particular interest. Our experiments on pure LCE have shown that the semisoftness parameter that measures the internal strain is proportional to the nematic order parameter. In photosensitive LCE under UV illumination the semisoftness parameter cannot be determined from the stress-strain curves due to strong inhomogeneity of the cis isomer concentration. So we exploited the fact that the director fluctuations are coupled to the anisotropy field and measured the change in the nematic order parameter as a function of UV illumination by measuring the relaxation rate of the director fluctuations with dynamic light scattering. We have also written holographic diffraction grating in photosensitive LCE and determined the depth of the layer that underwent cis-trans isomerization by measuring the angular width of the diffraction peak around the Bragg angle.