More than 1300 variables classified provisionally as first-overtone RR Lyrae pulsators in the MACHO variable-star database of the Large Magellanic Cloud (LMC) have been subjected to standard frequency analysis. Based on the remnant power in the prewhitened spectra, we found 70% of the total population to be monoperiodic. The remaining 30% (411 stars) are classified as one of nine types according to their frequency spectra. Several types of RR Lyrae pulsational behavior are clearly identified here for the first time. Together with the earlier discovered double-mode (fundamental and first-overtone) variables, this study increased the number of known double-mode stars in the LMC to 181. During the total 6.5yr time span of the data, 10% of the stars showed strong period changes.