  The localization kinetics of a regular block-copolymer of total length $N$
and block size $M$ at a selective liquid-liquid interface is studied in the
limit of strong segregation between hydrophobic and polar segments in the
chain. We propose a simple analytic theory based on scaling arguments which
describes the relaxation of the initial coil into a flat-shaped layer for the
cases of both Rouse and Zimm dynamics. For Rouse dynamics the characteristic
times for attaining equilibrium values of the gyration radius components
perpendicular and parallel to the interface are predicted to scale with block
length $M$ and chain length $N$ as $\tau_{\perp} \propto M^{1+2\nu}$ (here
$\nu\approx 0.6$ is the Flory exponent) and as $\tau_{\parallel} \propto N^2$,
although initially the characteristic coil flattening time is predicted to
scale with block size as $\propto M$. Since typically $N\gg M$ for multiblock
copolymers, our results suggest that the flattening dynamics proceeds faster
perpendicular rather than parallel to the interface, in contrast to the case of
Zimm dynamics where the two components relax with comparable rate, and proceed
considerably slower than in the Rouse case.
  We also demonstrate that, in the case of Rouse dynamics, these scaling
predictions agree well with the results of Monte Carlo simulations of the
localization dynamics. A comparison to the localization dynamics of {\em
random} copolymers is also carried out.
