  Conductance spectra measurements of highly transparent ramp-type junctions
made of superconducting $La_{2-x}Sr_{x}CuO_4$ electrodes and non
superconducting $La_{1.65}Sr_{0.35}CuO_4$ barrier are reported. At low
temperatures below $T_c$, these junctions have two prominent Andreev-like
conductance peaks with clear steps at energies $\Delta_1$ and $\Delta_2$ with
$\Delta_2 > 2\Delta_1$. No such peaks appear above $T_c$. The doping dependence
at 2 K shows that both $\Delta_1$ and $\Delta_2$ scale roughly as $T_c$.
$\Delta_1$ is identified as the superconducting energy gap, while a few
scenarios are proposed as for the origin of $\Delta_2$.
