Electron-electron-nuclear three-spin mixing occurs in radical pairs in solid-state matrices if the radicals feature a significant electron-electron spin coupling and an anisotropic hyperfine coupling. The perturbation of nuclear frequencies by the electron-electron spin coupling and the three-spin mixing have to be generally considered in the calculation of transition frequencies and probabilities in such radical pairs. Analytical descriptions of three-spin mixing for different ratios of the spin Hamiltonian parameters are introduced. It is found that nuclear frequencies are strongly perturbed if the difference of the Zeeman energies of the two electron spins is matched to half the hyperfine coupling and that three-spin mixing is maximum, if also the nuclear Zeeman frequency matches the former two interactions. Such double matching situations may be encountered for pairs of organic radicals under the conditions when transient electron spin resonance (ESR) experiments an usually performed. If three-spin mixing is significant, spin-correlated radical pairs are born in a state that features nuclear coherence in addition to the electron spin zero-quantum coherence that is created irrespective of this mixing. The possibility is discussed to detect such chemically induced nuclear coherence (CINC) in transient electron spin resonance experiments by selective microwave irradiation. It is shown that subsequent electron transfer reactions can yield chemically induced dynamic nuclear coherence (CIDNC) in isolated radicals and chemically induced dynamic nuclear polarization (CIDNP) in diamagnetic products if three-spin mixing is significant. The novel CINC, CIDNC, and CIDNP effects in the solid state might be used in the structure determination of spin-correlated radical pairs with applications to photosynthesis research.