  We extend the classical Avez-Seifert theorem to trajectories of charged test
particles with fixed charge-to-mass ratio. In particular, given two events
x_{0} and x_{1}, with x_{1} in the chronological future of x_{0}, we find an
interval I=]-R,R[ such that for any q/m in I there is a timelike connecting
solution of the Lorentz force equation. Moreover, under the assumption that
there is no null geodesic connecting x_0 and x_1, we prove that to any value of
|q/m| there correspond at least two connecting timelike solutions which
coincide only if they are geodesics.
