An isotropic and homogeneous cosmological model with a source of dark energy is studied. That source is simulatedwith a viscous relativistic fluidwith minimal causal correction. In this model the restrictions on the parameters coming from the following conditions are analized: (a) energy density without singularities along time, (b) scale factor increasing with time, (c) universe accelerated at present time, (d) state equation for dark energy with "omega" bounded and close to -1. It is found that those conditions are satisfied for the following two cases. (i) When the transport coefficient (tau(Pi)), associated to the causal correction, is negative, with the additional restriction zeta |tau(Pi)| >2/3, where. is the relativistic bulk viscosity coefficient. The state equation is in the "phantom" energy sector. (ii) For tau(Pi) positive, in the "k-essence" sector. It is performed an exact calculation for the case where the equation of state is constant, finding that option (ii) is favored in relation to (i), because in (ii) the entropy is always increasing, while this does no happen in (i).