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We present the results from Fabry-Perot imaging spectroscopy of the Balmer-dominated supernova remnant DEM L71 (0505-67.9) in the LMC. Spectra extracted from the entire circumference of the blast wave reveal the broad- and narrow-component Hα line emission characteristic of nonradiative shocks in partially neutral gas. The new spectra of DEM L71 include portions of the rim that have not been previously observed. We find that the broad-component width varies azimuthally along the edge of DEM L71, ranging from 450±60 km/s along the eastern edge to values as high as 985⁺²¹⁰_–165km/s along the faint western edge. The latter width is nearly 60% larger than the value determined by earlier spectroscopy of the brightest Balmer-dominated filaments. In part of the faint northern rim the broad component is not detected, possibly indicating a lower density in these regions and/or a broad-component width in excess of 1000 km/s. Between the limits of zero and full electron-ion temperature equilibration at the shock front, the allowed range of shock velocities is 430-560 km/s along the east rim and 700-1250 km/s along other parts of the blast wave. The Hα broad-to-narrow flux ratios vary considerably around the remnant, ranging from 0.4 to 0.8. These ratios lie below the values predicted by our shock models. We find that narrow-component Hα emission from a cosmic-ray precursor may be the cause of the discrepancy. The least decelerated portions of the blast wave (i.e., regions excluding the brightest filaments) are well characterized by Sedov models with a kinetic energy E₅₁=(0.37±0.06)D^5/2₅₀, where D₅₀is the LMC distance in units of 50 kpc. The corresponding age for DEM L71 is (4360±290)D₅₀yr. This is the first time that velocity information from the entire blast wave has been utilized to study the global kinematics of a nonradiative supernova remnants at a known distance.