Linear and nonlinear theories of amplified spontaneous emission in longitudinally-pumped semiconductor lasers have been developed. Spatial inhomogeneity in three dimensions and spectral inhomogeneity of gain and spontaneous emission are taken into account. Experiments to investigate the dependency of lasing threshold and differential efficiency of electron-beam-pumped semiconductor lasers on excited region diameter have been performed. The results of threshold measurements have agreed well with the linear theory calculations, while accounting for the results of differential efficiency measurements has required the development of a nonlinear theory. The data for non-linear calculations were provided by experiments on saturation of spontaneous emission. The results of experiments have definitely proved the inhomogeneity of gain. Based on the data obtained from experiments, the nonlinear calculations have explained the dependence of differential efficiency on the excited region diameter.