Instabilities of a coherent state of Wannier-Mott excitons sustained by a resonant pumping wave in cavity and cavityless cases are analysed. In particular, instability with respect to spatially periodic stratification can exist. The period of such stratification is L approximately L_ex=(h(cross)/m gamma )¹2/, where m is the effective exciton mass, and gamma is the reciprocal exciton lifetime. The results of numerical modelling of corresponding non-linear structures are presented. For 'exciton-pumping' bistability, non-monotonic switching fronts are demonstrated numerically.