  In this Letter we present new tunneling data on YBa$_2$Cu$_3$O$_7$ thin films
by low temperature scanning tunneling spectroscopy. Unusual peak-dip-hump
features, previously reported in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, are also
found in YBa$_2$Cu$_3$O$_7$. To analyse these common signatures we propose a
new heuristic model in which, in addition to the d-wave symmetry, the gap
function is energy dependent. A simple expression for the quasiparticle density
of states is derived, giving an excellent agreement with the experiment. The
dynamics of the quasiparticle states and the energy scales involved in the
superconducting transition are discussed.
