In an effort to quantitatively examine the effect of coupling between multiple relaxation modes, a new model involving two coupled Maxwell modes is developed as a generalization of the upper-convected Maxwell and the Giesekus models. The model contains, in addition to the parameters inherent to a Maxwell model with two uncoupled modes (i.e., lambda(1),lambda(2) and eta(1) = G(1) lambda(1), eta(2) = G(2) lambda(2)), a dimensionless coupling coefficient theta that multiplies a quadratic coupling term. In the two characteristic limits theta = 0 or (eta(1),lambda(1)) = (eta(2),lambda(2)), the Maxwell model with two uncoupled relaxation modes or the Giesekus constitutive model is obtained, respectively. The rheological behavior of the model is investigated in the linear and nonlinear deformation-rate regimes. Calculation of the linear viscoelastic behavior shows that the linear stress relaxation modulus is the sum of two decaying exponentials with characteristic times and preexponential factors that are quite different from lambda(1), lambda(2) and G(1), G(2), respectively. In slow, slowly varying flows, the zero shear-rate ratio Psi(2)(0)/Psi(1)(0) assumes small negative values when theta takes on small positive values. The nonlinear rheological behavior of the model is examined under the imposition of shear and extensional flow fields, from both a steady-state and transient perspective. The qualitative behavior observed is remarkably rich in describing the experimental trends seen in polymer melts and Boger fluids for a constant value of theta approximate to 0.1.