Thermodynamic characteristics of inelastic deformation (work W def, heat Q def, and stored energy ΔU def) are studied for aromatic main-chain copolyesters (CPEs) based on p-hydroxybenzoic acid and poly(ethylene terephthalate) (Rodrun and SKB-1), p-hydroxybenzoic acid, naphthalene carboxylic acid, and terephthalic acid with hydroquinone and dioxyphenyl (HX-6000 and HX-7000). The samples are deformed under an active uniaxial compression by ɛdef ≈ 50% at room temperature. All CPEs are semicrystalline polymers; their degree of crystallinity is (depending on their prehistory) 5–30%, and the melting temperature of crystallites is 275–350°C. Seemingly, the glassy component of CPEs includes two interpenetrating glassy structures, S-1 and S-2, with different glass-transition temperatures Tg: 90–120 and 250–270°C, respectively. During loading, all coexisting crystalline and glassy structures of CPEs store residual strain ɛres. The kinetics of the temperature-stimulated strain recovery of ɛres is measured. In component S-1, strain recovery occurs in the temperature interval ranging from T room to 120°C. In the crystalline phase, this process occurs in the melting-temperature interval. In component S-2, strain recovery ɛres commences at T > 120°C. In CPEs, all structural components are involved in deformation at different ɛdef. At small strains only component S-1 is deformed; then, at ɛdef ≈ 10–15%, component S-2 is involved in the deformation. Crystallites join this process at ɛdef > 20–25% (ɛ y = 8–10%). In CPE, two modes of deformation arise: reversible elastic (retarded elastic) and true plastic irreversible deformation. True plastic permanent strain always exists in the deformed CPEs. Deformation of all CPEs proceeds easier than that of all “common” glassy polymers (polystyrene, poly(methyl methacrylate), etc.). In CPEs, the yield stress and compressive modulus appear to be ≈40–50% lower than in “common” glassy polymers. It seems that the mesomorphic structure of LC CPEs enhances the elementary plastic processes in them. Thermodynamic characteristics of the S-1 phase plasticity are compared with the behavior of “common” glassy polymers. At the early stages of loading, nearly all mechanical work of deformation W def spent is stored in phase S-1 in the form of δU def, as in all “common” glassy polymers. This fact implies that the inelastic deformation of LC glasses commences with the nucleation of small-scale and localized intermolecular transformations of the nonconformational type. In both mesomorphic and “common” glassy polymers, the stage of nucleation of such transformations controls the overall kinetics of the inelastic and plastic deformation. Nucleation does not depend on chain rigidity, a circumstance that conflicts with the model of forced elasticity. It seems that crystallites in CPE are deformed according to crystallographic mechanisms. Currently, neither the structure nor the deformation mechanism of component S-2 is known.