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Schwarz's method to construct off-mass-shell amplitudes is extended to two-body scattering amplitudes with arbitrary external masses in the Veneziano and Neveu-Schwarz models. It is shown that ghost-free amplitudes are obtainable by replacing linear t-channel trajectories by s-dependent ones in the Veneziano amplitudes and the Neveu-Schwarz ones respectively. It is also shown that transversely polarized integer spin particles can be introduced as one of initial or final two particles. Indoi:10.1143/ptp.54.268 fatcat:jt4zw7ajbbcrpiwzd3yoj3wrha