  Particle acceleration is expected to be different between relativistic and
non-relativistic collisionless shocks. We show that electromagnetic
counterparts to gravitational waves (GWs), gamma-ray burst (GRB) afterglows,
are ideal targets for observing trans-relativistic evolution of accelerated
electron distribution because the GWs spot nearby GRBs with off-axis jets,
otherwise missed in gamma-ray observations. We find that the relativistic
spectral slope begins to change steeply near the peak time of the light curve
and approaches the non-relativistic limit in about 10 times the peak time. The
trans-relativistic evolution of the afterglow synchrotron spectrum is
consistent with GRB 170817A observations within errors, and will be measurable
in similar but more distant events at a GW horizon $\sim 200$ Mpc in a denser
environment. We roughly estimate that such events represent a fraction of 10-50
per cent of the GRB 170817A-like off-axis short GRBs. We also find that the
spectral evolution does not depend on the jet structure if their light curves
are similar to each other.
