The decay of Xe137 was studied by means of scintillation techniques. The radioactive samples were produced by means of neutron irradiation of natural xenon, which contains 8.87% Xe136. The half-life of Xe137 was found to be 3.95+/-0.11 min. One gamma ray of 0.455+/-0.003 MeV was attributed to Xe137. An upper limit of 0.03 of the intensity of this gamma ray is placed on any other gamma ray due to the decay of Xe137. The end-point energy of the beta spectrum was found to be 4.06+/-0.06 MeV using K42 as a calibration check. A beta ray was found to be in coincidence with the 0.46-MeV gamma ray. A Kurie plot of the beta-gamma coincidence spectrum as well as a subtraction method of the singles Kurie plot were both in agreement with 3.60+/-0.06 MeV for the lower-energy beta group. In order to get the intensity of the two beta transitions, two independent methods were utilized. These indicated a relative intensity of about 0.33+/-0.03 for the 3.60-MeV beta-ray group and 0.67+/-0.03 for the 4.06-MeV beta-ray group. Logft values indicate first-forbidden beta-ray selection rules for both transitions. This is found to be in accord with shell-model predictions. A decay scheme is proposed on the basis of these results.