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Abstract. The present study is devoted to the statement of compatibility conditions on propagating wave sur-faces of strong and weak discontinuities in thermoelastic continua with microstructure. The field formalism is used to study the problem. A natural density of thermoelastic action and the corresponding variational least action principle are stated for a varying domain. A special form of the first variation of the action is employed to obtain 4-covariant boundary conditions on the wave surfaces. These are given by jumps of the Piola-Kirchhoff stress 4-tensor and the energy-momentum tensor. Problems of propagation of weak discontinuities in type-II MPTE continua are considered. Geometrical and kinematical compatibility conditions are used to study possi-ble wave surfaces of weak discontinuities. It is shown that the surfaces of weak discontinuities can propagate without weak discontinuities of the temperature displacement.

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