Lord-Shulman's system of partial dierential equations of generalized thermoelasticity (1) is considered, in which the Þnite velocity of heat propagation is taken into account by introducing a relaxation time constant. General aspects of the theory of boundary value and initial-boundary value problems and representation of so- lutions by series and quadratures are considered using the method of a potential. As one knows, in the classical theory of thermoelasticity the velocity of heat propagation is assumed to be inÞnitely large. However, in study- ing dynamic thermal stresses in deformable solid bodies, when the inertia terms in the equations of motion cannot be neglected, one must take into account that heat propagates not with an inÞnite but with a Þnite velocity; a heat sow arises in the body not instantly but is characterized by a Þnite relaxation time. Presently, there are at least two dierent generalizations of the classical theory of thermoelasticity: the Þrst of them, Green-Lindsay's generalization (1) is based on using two heat relaxation time constants; the other one, Lord-Shulman's generalization (2) admits only one relaxation time constant. Both generalizations were developed as an attempt at ex- plaining the paradox of the classical case that the heat propagation velocity is an inÞnite value. In this paper, based on (3), we develop a general theory of solvability, as well as of construction of approximate and eective solutions of dynamic problems for the conjugate system of dierential equations of thermoelastic- ity proposed by Lord and Shulman (LAS theory). Green-Lindsay's theory (G A L-theory) is developed in (4, 5).