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We r e p o r t on measurements of quantum electrodynamic processes in an intense electromagnetic wave, where nonlinear e ects (both multiphoton and vacuum polarization) are prominent. Nonlinear Compton scattering and electronpositron pair production have been observed in collisions of 46.6 GeV and 49.1 GeV electrons of the Final Focus Test Beam at SLAC with terawatt pulses of 1053 nm and 527 nm wavelengths from a Nd:glass laser. Peak laser intensities of 0:5 10 18 W/cm 2 have been achieved, corresponding to a value of 0:4 for the parameter = eErms=m!0c, and to a value of 0:25 for the parameter e = E ? rms =Ecrit = eE ? rms h=m 2 c 3 , where E ? rms is the rms electric eld strength of the laser in the electron rest frame. We p r e s e n t data on the scattered electron spectra arising from nonlinear Compton scattering with up to four photons absorbed from the eld. A convolved spectrum of the forward high energy photons is also given. The observed positron production rate depends on the fth power of the laser intensity, as expected for a process where ve photons are absorbed from the eld. The positrons are interpreted as arising from the collision of a high-energy Compton scattered photon with the laser beam. The results are found to be in agreement with theoretical predictions.