On the basis of kinetic theory, the stability of an electron beam interacting with inhomogeneous plasma is investigated at Knudsen numbers of the order of 1. The theory has been tested on the example of a low-voltage beam discharge in a rear gas. It is shown that in the case of an inhomogeneous plasma even if the attenuation of a beam is neglected, several perturbations can propagate simultaneously at the same frequency, but with different phase and group velocities and increments. The case of a linear dependence of the plasma density on the coordinate is investigated in detail. In this case, there are two solutions: n- and p-waves, only the n-wave having a physical meaning. It is found that an increase in the plasma density gradient leads to a decrease in the increment and an increase in the phase and group velocities of propagation of perturbations with a frequency of the order of plasma frequency. A system with a growing plasma density along the beam direction is more stable than that with a constant density. For a significant change in the growth rate of the disturbance, the relative gradient of plasma density by an amount of about 10% at the wavelength is sufficient. All the observed features of the perturbation parameters depending on the plasma density gradient are physically interpreted. The calculations are confirmed by experimental data.