As a first step in characterizing molecular Rydberg states in the solid state, the absorption spectra arising from acetylene and benzene impurity states in solid krypton and argon in the far-ultraviolet region have been obtained. The first member of the acetylene Rydberg series, which appears at 8.155 eV in the gas phase, is observed to be shifted to 8.67 eV in a krypton matrix and to 9.01 eV in an argon matrix. These large energy shifts are discussed, particularly with reference to the optical spectra of rare-gas solids and rare-gas alloys, where similar large blue shifts are observed. The far-ultraviolet spectra of benzene trapped in krypton and argon matrices show a qualitatively different phenomenon. The Rydberg states of benzene are observed to interact with conduction-band continuum states to exhibit anomalous Fano-type line shapes. The Rydberg states repulse the neighboring continuum states to produce sharp decreases in the continuum absorption intensity. These results are discussed in connection with other systems which show Fano-type line shapes.