We study both theoretically and experimentally the magnetization loss of a nuclear spin system irradiated with a rf field under a linear field sweep through the resonance. Two limiting cases are considered. The first is that of a slightly saturating passage, in which the loss is simply related to the rf field amplitude, a fact which allows an easy calibration of the latter. The second case is that of a quasiadiabatic passage which reverses the magnetization. Three factors contribute to the magnetization loss: (1) The passage is sudden far in the wings of the line, and it becomes rather abruptly adiabatic at a given distance from resonance. An entropy increase accompanies this transition. (2) The passage through the central part is not quite adiabatic because of the finite sweep rate of the field through the line. (3) The finite spin-lattice relaxation time of the spin-spin term causes a loss of magnetization at the passage on the line. The losses are numerically computed for the fluorine spin system in CaF2 with H0∥, and they are found to agree with the experimental values.