  The dynamic entropic repulsion for the Ginzburg-Landau $\nabla\phi$ interface
model was discussed in [Deuschel-N. 2007] and the asymptotics of the height of
the interface was identified. This paper studies a similar problem for two
interfaces on the wall which are interacting with one another by the exclusion
rule. Each leading order of the asymptotics of height is $\sqrt{\log t}$ as
$t\to\infty$ for the system on $\integer^d,\,d\ge3$, $\log t$ for the system on
$\integer^2$. The coefficient of the leading term for each interface is also
identified.
