  Electrons accelerated in relativistic collisionless shocks are usually
assumed to follow a power-law energy distribution with an index of $p$.
Observationally, although most gamma-ray bursts (GRBs) have afterglows that are
consistent with $p>2$, there are still a few GRBs suggestive of a hard ($p<2$)
electron energy spectrum. Our previous work showed that GRB 091127 gave strong
evidence for a double power-law hard electron energy (DPLH) spectrum with
$1<p_1<2$, $p_2>2$ and an "injection break" assumed as $\gamma_{\rm b}\propto
\gamma^q$ in the highly relativistic regime, where $\gamma$ is the bulk Lorentz
factor of the jet. In this paper, we show that GRB 060614 and GRB 060908
provide further evidence for such a DPLH spectrum. We interpret the multi-band
afterglow of GRB 060614 with the DPLH model in an homogeneous interstellar
medium by taking into account a continuous energy injection process, while for
GRB 060908, a wind-like circumburst density profile is used. The two bursts,
along with GRB 091127, suggest a similar behavior in the evolution of the
injection break, with $q\sim0.5$. Whether this represents a universal law of
the injection break remains uncertain and more such afterglow observations are
needed to test this conjecture.
