<p>We develop an effective mathematical model for the macroscopic viscoelastic behaviour of nematic liquid crystal elastomers under external loading. In this model, elastic and viscous contributions due to large-strain deformations of the polymeric network and rotations of the liquid crystal director are defined, allowing for the separate yet interacting mechanisms to be represented within a unified constitutive framework. A distinct feature of our approach is the multiplicative decomposition of the macroscopic deformation gradient for the nematic elastomer and the local deformation tensor due to the underlying polymeric network into an elastic and a viscous component. A finite element method is formulated and implemented to approximate computationally the behaviour of these materials and demonstrate the effect of different model parameters in loading and unloading.</p>