Several new progressions consisting of broadbands were obsd. in the absorption spectra of NO trapped in rare gas matrixes. They were identified as the blue shifted transitions to the n = 3 (A 2S+, C 2P, D 2S+) and n = 4 (E 2S+, K 2P, M 2S+) Rydberg states of NO in Ne matrixes and to the n = 3 Rydberg states in Ar, Kr, and Xe matrixes. Linewidths (50 to 180 meV) and matrix shifts (0.3 to 1.2 eV) decrease from Ne to Xe matrixes. For each matrix, the shifts decrease according to the symmetry of the excited state orbital, in the sequence ss-ps-pp. An attempt to apply the quantum defect formula with values, for the Rydberg const. and the ionization potential of the matrix isolated mol. taken from lit., fails to describe the vertical transition energies of n = 3 and n = 4 states in Ne matrixes. By using the adiabatic energies of 3ss and 4ss states to generate a series shows that the vertical transitions of n >= 5 states lie in the ionization continuum. This could explain the nonobservation of n >4 states in Ne matrixes. In the heavier matrixes, this model predicts n = 4 states, but their existence is not borne out by expt. The Wannier model also fails to describe these transitions. [on SciFinder (R)]