The dispersion characteristics of the TM-type non-linear surface electromagnetic waves at the boundary of a magnetoactive semiconductor and a uniaxial non-linear medium (Voigt geometry) have been studied. A new type of wave, i.e. a non-resonance non-linear surface wave, has been revealed. The exact criteria for their existence have been formulated. The means to control their characteristics have been shown and the ranges of multivalues of their dispersion curves have been determined. Calculation of a three-mirror open resonator with a non-linear boundary has been carried out. The domains of the system parameters corresponding to the emergence of unstable solutions have been defined. In addition, their correlation with the surface concentrations and the mobility of the major charge carriers in the semiconductor and the open resonator coupling coefficient with the semiconductor under investigation has been established. The results of experimental studies of the surface characteristics of narrow-gap n-type Cd xHg 1- xTe samples are discussed.