At least three large earthquakes in 1978 and 1980 near Long Valley caldera have unusual non-double couple mechanisms, unlike those appropriate for shear faulting. This conclusion is supported by short-period P first motions, long-period P and SH first motions, surface wave spectral amplitudes and initial phases, and long-period P and SH waveforms. Two explanations for these anomalous mechanisms have been proposed: (1) simultaneous strike slip and normal motion on separate faults and (2) tensile failure under high fluid pressure. To evaluate these conflicting hypotheses we have inverted P and SH wave-forms recorded by the Global Digital Seismograph Network (GDSN) to obtain moment tensors for the earthquakes and have also generated broadband seismograms by deconvolving short- and long-period GDSN data. The largest event (1633:44 UTC, May 25, 1980) has a duration of about 20 s and can be resolved into three events, separated by intervals of about 7 and 10 s, each having a non-double-couple mechanism. This contrasts with previously reported inversion results for other complex earthquakes, all of which have double-couple subevents. Furthermore, the earthquake of 1450:56 UTC May 27, 1980, appears to be simple and not composed of smaller events. Thus the non-double-couple mechanisms are probably intrinsic to the source process and not artifacts caused by misinterpretation of multiple ruptures as single events. Rapid opening of cracks under high fluid pressure is a likely possibility for this process, although its dynamics are complex and not yet fully understood.