  We study the time evolution of classical spin systems with purely
relaxational dynamics, quenched from T >> T_c to the critical point, in the
semi-infinite geometry. Shortly after the quench, like in the bulk, a
nonequilibrium regime governed by universal power laws is also found near the
surface. We show for `ordinary' and `special' transitions that the
corresponding critical exponents differ from their bulk values, but can be
expressed via scaling relations in terms of known bulk and surface exponents.
To corroborate our scaling analysis, we present perturbative
(epsilon-expansion) and Monte Carlo results.
