This paper is aimed at investigating the influence of nonviscous modes on the vibrational response of viscoelastic systems. Thus, exponential damping models are considered. Provided that nonviscous modes disappear with time, they have influence on only the transient response of the system. Thus, the system response is obtained by means of modal superposition in order to examine the contribution of each mode. The analysis is carried out on two lumped parameter systems; systems involving a single degree and three degrees of freedom are studied. For the former, the analytic solution is derived via modal superposition and Laplace transformation. For the latter, the analytic response is contrasted with that provided via two numerical direct methods. From this investigation, it can be concluded that the system may present no oscillations, even if elastic modes are underdamped modes.