We have synthesized and studied the CD spectra of five new double-stranded RNA polymers: poly[r(A-G)·r(C-U)], poly[r(A-U-C)·r(G-A-U)], poly[r(A-C-U)·r(A-G-U)], poly[r(A-A-C)·r(G-U-U)], and poly[r(A-C-C)·r(G-G-U)]. Together with previously published spectra of seven other RNA sequences, the spectra of these new sequences provide a library sufficient to approximate the spectra of all other RNA sequences by first-neighbor formulas and, in addition, give four spectra with which we may test the validity of first-neighbor approximations. (1) We find that the spectra of RNA sequence isomers are very different, but that the spectra essentially do obey first-neighbor relationships. (2) We have derived tentative first-neighbor assignments of negative bands at about 295 and 210 nm in the CD spectra. (3) A test of spectral independence shows that among the 12 polymer spectra there are at least seven significant independent spectral shapes, one less than the eight needed to give the most accurate spectral analysis of an unknown RNA sequence for its first-neighbor frequencies. (4) Spectra are calculated for RNAs of random base composition, approximating natural RNAs having complex sequences. (5) A T-matrix of spectral components assigned to the first-neighbor base pairs is derived from 10 of the spectra. This matrix allows an estimation of the CD spectrum of any other known RNA sequence or an analysis of the spectrum of an unknown sequence for its distribution of first-neighbor base-pair frequencies. (6) Test analyses of two of the synthetic polymers and of two natural RNAs set a probable limit on the accuracy of first-neighbor frequency determinations using this T-matrix. (7) Finally, we summarize in an appendix the melting temperatures for all the RNA and corresponding DNA sequences; it appears that the Tm values of both DNAs and RNAs approximately obey first-neighbor relationships.