We report on very high energy gamma-ray observations with the MAGIC Telescope of the pulsar PSR B1951+32 and its associated nebula, CTB 80. Our data constrain the cutoff energy of the pulsar to be less than 32 GeV, assuming the pulsed gamma-ray emission to be exponentially cut off. In the case that the cutoff follows a superexponential behavior, the cutoff energy can be as high as similar to 60 GeV. The upper limit on the flux of pulsed gamma-ray emission above 75 GeV is 4.3; 10(-11) photons cm(-2) s(-1), and the upper limit on the flux of steady emission above 140 GeV is 1.5; 10(-11) photons cm(-2) s(-1). We discuss our results in the framework of recent model predictions and other studies.
