We observed substantial dispersion in the breakdown electric field for yttria stabilized cubic zirconia (Zr0₂). The measured breakdown field at 1064 run is a factor of 5 larger than that at 532 nm for 18 nsec (FWHM) pulses. For 532 run pulses, we measured a significant decrease in transmission prior to the observation of catastrophic damage (i.e., damage accompanied by a spark and fracture of the sample). The observed nonlinear transmission is attributed to absorption by color centers generated by two-photon absorption (2PA). Presence of the color centers were directly monitored by transmission measurements. A permanent change in transmission was measured by irradiating the samples at high intensities (300 MW/cm²). These induced defects are long lived (on the order of hours) but can be bleached by repeated irradiation with relatively low intensities (20 MW/cm²). In a separate experiment, using picosecond pulses at 532 nm, the 2PA coefficient was determined to be 0.015 cm/GW.