Isothermal vapor-liquid equilibria (VLE) for methanol-1,1-dimethylethyl methyl ether (tert-butyl methyl ether or MTBE) and for methanol-1,1-dimethylpropyl methyl ether (tert-amyl methyl ether or TAME) measured at temperatures ranging from 288.15 to 338.15 K have been correlated by means of the UNIQUAC model and by means of the Peng-Robinson equation of state and the Wong-Sandler mixing rule. The systems show positive deviations from Raoult’s law with an azeotrope, whose coordinates have been interpolated and compared with experimental values. Predictions of VLE data and azeotrope coordinates have been made by means of several versions of the group contribution UNIFAC model and by means of the modified Huron-Vidal second order (MHV2) model used in conjunction with the same UNIFAC model versions. In order to study the effect of the hydrogen-bond interaction in these mixtures, the lattice-fluid associated solution (LFAS) model and the extended real associated solution (ERAS) model have been used to simultaneously describe excess enthalpy and VLE data. Results from these calculations have been compared with those obtained by means of the purely physical lattice-fluid model (LF) of Sanchez-Lacombe.