The evolution and establishment of the boundary current near the weste
rn coast of the ocean in considered. Two types of the establishment ar
e identified, depending on the relation between the Rossby radius of d
eformation, L(R), and the Munk scale, L(M). When L(R) much greater tha
n L(M) (barotropic mode) the establishment is governed by the properti
es of Rossby waves and proceeds in two stages. First the boundary curr
ent is established. Then the reflected wave is attenuated due to visco
sity. When L(R) less than or equal to L(M) (baroclinic modes) the refl
ected wave is not formed and the time-dependent solution evolves slowl
y towards Munk's steady-state solution. Characteristic time scales for
the establishment of the boundary current are derived.