We demonstrate the use of a delay-asymmetric nonlinear loop mirror (DANLM) for tunable differential phase shift keying (DPSK) demodulation. The DANLM introduces tunable differential delay between two counterpropagating signals while maintaining their phase information. The device is demonstrated using degenerate four-wave mixing wavelength-conversion and wavelength-dependent group delay. The DANLM can support the demodulation of DPSK signals over a wide range of continuously tunable bit rates and delays. We experimentally achieve the demodulation of return-to-zero DPSK signals at 10 and 20 Gbits/s using the same DANLM. Demodulation of nonreturn-to-zero DPSK signal at 10 Gbits/s with one-, half-, and quarter-bit delays has also been demonstrated. Widely opened eye diagrams and error-free detection have been obtained.