A very interesting model for relativistic scattering ampli tude has been recently proposed by VE~EZlA~O (1), in which crossing symmetry and Regge asymptotic behavfour are ensured by the requirement of l inearly rising trajectories. The scattering amplitude exhibits Regge poles in families of parallel trajectories with residues in definite ratios, and satisfies generalized supereonvergence relations. In this note, we discuss the implication of the model when applied to different processes, and show how the constraints imposed on the Regge trajectories give rise to mass relations. Wi th this aim, we generalize slightly the expression given by VENEZ~A~O for the scattering amplitude, in such a way that it can be applied to processes of different types. We shall restrict here to those processes in which each channel is dominated by a single trajectory. The inclusion of more trajectories in the same channel, owing to the rather stringent conditions imposed by the model, makes a solution possible only in the case of degenerate trajectories. We keep the hypothesis of linearly rising trajectories, and follow the approximation of real trajectory functions, which is equivalent to narrow-width resonance approximation. We shall consider the following types of processes: