We have applied exciton theory to estimate the circular dichroism (CD) contribution of the Trp Bb transition to the far-UV circular dichroism of globular proteins. Strong exciton couplets are predicted for a number of proteins, including dihydrofolate reductase (DHFR), chymotrypsin and chymotrypsinogen. These predicted CD spectra are dominated by the contributions of the closest pair, W47-W74 in DHFR and W174-W215 in chymotrypsinogen. The sign and magnitude of the predicted couplets are consistent with experimental data for DHFR and its W74L mutant, and with the previously unexplained CD changes upon chymotrypsin activation. More extensive coupled-oscillator interactions among all aromatic and peptide chromophores are described for DHFR and barnase. The total far-UV CD spectra predicted for these proteins agree poorly with experiment, primarily owing to difficulties in the calculation of the peptide CD. Nevertheless, difference spectra calculated between the wild-type spectra and those of mutants in which individual aromatic residues are replaced with non-chromophoric side chains show satisfactory agreement with experiment in most cases.