The enthalpy relaxation of a series of linear amorphous polyesters (poly(propylene isophthalate) (PPIP), poly(propylene terephthalate) (PPTP), poly(ethylene terephthalate) (PETP), and poly(dipropylene terephthalate) (PDPT)) has been investigated by differential scanning calorimetry (DSC). These polyesters have been annealed at equal undercooling below their respective glass transition temperatures, T-g, (T-g-27 degrees C, T-g-15 degrees C, and T-g-9 degrees C) for periods of time from 15 min to 480 h. The key parameters of structural relaxation, namely the apparent activation energy (Delta h*), the nonlinearity parameter (x) and the nonexponentiality parameter (beta), have been determined for each polyester and related to an effective relaxation rate (1/tau(eff)) and to the chemical structure. We observe that the variation of the structural relaxation parameters shows a trend that is common to other polymeric systems, whereby an increase of x and beta corresponds a decrease in Delta h*. The comparison of these parameters in PETP and in PPTP gives information about the effect of the introduction of a methyl group pendant from the main chain; the x parameter increases (i.e., a reduced contribution of the structure to the relaxation times), beta increases (i.e., a narrow distribution of relaxation times), and Delta h* decreases. Additionally, enthalpy relaxation experiments show that a decrease of Delta h* correlates with an increase of 1/tau(eff), when they are measured at a fixed value of the excess enthalpy, delta(H). The introduction of an isopropyl ether group in PDPT with respect to PPTP decreases both x and beta, but increases Delta h*, which the rate of relaxation decreases. The ring substitution in PPTP and PPIP originates less significant changes in the structural parameters.