Abstract: In an experiment performed at the Princeton-Pennsylvania Accelerator with scintillation counters and spark chambers, we have determined the branching ratios for the K+ decay modes Kμ2+, Kπ2+, Kμ3+, and Ke3+. For each event, we measured the momentum and range of the charged secondary and the time interval between the arrival of the K+ and its decay. The momentum was measured in thin-foil spark chambers placed in a magnetic field. The range was then measured in a thick-plate spark chamber in which all charged products from K+ decay were stopped. K+ decays in flight were eliminated through use of the timing information. The solid angle and detection efficiency of the apparatus were constant over the momentum interval 130 to 260 MeVc. Based on approximately 23 000 measured events, our values for the branching ratios are (63.34+/-0.44)% for Kμ2+, (20.59+/-0.40)% for Kπ2+, (4.97+/-0.16)% for Ke3+, and (3.82+/-0.29)% for Kμ3+. These values have been determined by using for the τ and τ' branching ratios (5.58+/-0.08)% and (1.70+/-0.055)%, respectively. A table of weighted averages of all K+branching-ratio measurements is included.