  We study analytically, via the Newman-Penrose formalism, the late-time decay
of linear electromagnetic and gravitational perturbations along the event
horizon (EH) of black holes. We first analyze in detail the case of a
Schwarzschild black hole. Using a straightforward local analysis near the EH,
we show that, generically, the ``ingoing'' ($s>0$) component of the perturbing
field dies off along the EH more rapidly than its ``outgoing'' ($s<0$)
counterpart. Thus, while along $r=const>2M$ lines both components of the
perturbation admit the well-known $t^{-2l-3}$ decay rate, one finds that along
the EH the $s<0$ component dies off in advanced-time $v$ as $v^{-2l-3}$,
whereas the $s>0$ component dies off as $v^{-2l-4}$. We then describe the
extension of this analysis to a Kerr black hole. We conclude that for axially
symmetric modes the situation is analogous to the Schwarzschild case. However,
for non-axially symmetric modes both $s>0$ and $s<0$ fields decay at the same
rate (unlike in the Schwarzschild case).
