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The theory of the influence on angular correlations of perturbing interactions in the intermediate state is reformulated to allow the description of the effects of time-dependent as well as of static perturbations. For static interactions of the nuclear electric quadrupole moment with crystalline fields of axial symmetry in polycrystalline sources, attenuation factors are calculated for the coefficients of the various terms in the expansion of the correlation function in Legendre polynomials. No matter how strong the quadrupole interaction, some anisotropy must remain for polycrystalline sources but, for the same interaction in simple single crystals, the anisotropy can be either undisturbed or completely destroyed, depending on the orientation of the crystal. Fields of lower symmetry are shown also to leave, for polycrystalline sources, some anisotropy. Expressions for the influence of randomly fluctuating interactions, such as must exist in liquid sources, are calculated and these predict arbitrarily complete destruction of the correlation under certain conditions, but explain the more nearly unperturbed results usually found with such sources. For electronic shells having magnetic moments, the influences of electronic paramagnetic relaxation and of anisotropy of the hyperfine structure interaction are examined. An applied static magnetic field in the presence of static quadrupole interactions in polycrystalline sources is shown to have differing effects depending on the relative strengths of the two interactions. Application of a magnetic field directed toward a counter cannot reduce the disturbance of the intermediate state in liquid sources, except under special circumstances. The influences of an applied field in the presence of time dependent anisotropic hyperfine structure interactions are discussed. Finally, the feasibility of resonance experiments, for the precise determination of nuclear moments in the intermediate state, is explored.