Isothermal compression of a bubbly secondary fluid in a mixing-throat and diffuser is described by a one-dimensional flow model of a liquid-jet pump. Friction-loss coefficients used in the four equations may be determined experimentally, or taken from the literature. The model reduces to the liquid-jet gas compressor case if the secondary liquid is zero. Conversely, a zero secondary-gas flow reduces the liquid-jet gas and liquid (LJGL) model to that of the familiar liquid-jet liquid pump. A “jet loss” occurs in liquid-jet pumps if the nozzle tip is withdrawn from the entrance plane of the throat, and jet loss is included in the efficiency equations. Comparisons are made with published test data for liquid-jet liquid pumps and for liquid-jet gas compressors. The LJGL model is used to explore jet pump responses to two-phase secondary flows, nozzle-to-throat area ratio, and primary-jet velocity. The results are shown in terms of performance curves versus flow ratios. Predicted peak efficiencies are approximately 50 percent. Under severe operating conditions, LJGL pump performance curves exhibit maximum-flow ratios or cut-offs. Cut-off occurs when two-phase secondary-flow streams attain sonic values at the entry of the mixing throat. A dimensionless number correlates flow-ratio cut-offs with pump geometry and operating conditions. Throat-entry choking of the secondary flow can be predicted, hence avoided, in designing jet pumps to handle two-phase fluids.