  We find that motion in internal moduli spaces of generic domain walls has an
upper bound for its velocity. Our finding is based on our generic formula for
all-order effective actions of internal moduli parameter of domain wall
solitons. It is known that the Nambu-Goldstone mode $Z$ associated with
spontaneous breaking of translation symmetry obeys a Nambu-Goto effective
Lagrangian $\sqrt{1 - (\partial_0 Z)^2}$ detecting the speed of light
($|\partial_0 Z|=1$) in the target spacetime. Solitons can have internal moduli
parameters as well, associated with a breaking of internal symmetries such as a
phase rotation acting on a field. We obtain, for generic domain walls, an
effective Lagrangian of the internal moduli $\epsilon$ to all order in
$(\partial \epsilon)$. The Lagrangian is given by a function of the Nambu-Goto
Lagrangian: $L = g(\sqrt{1 + (\partial_\mu \epsilon)^2})$. This shows
generically the existence of an upper bound on $\partial_0 \epsilon$, i.e. a
speed limit in the internal space. The speed limit exists even for solitons in
some non-relativistic field theories, where we find that $\epsilon$ is a type I
Nambu-Goldstone mode which also obeys a nonlinear dispersion to reach the speed
limit. This offers a possibility of detecting the speed limit in condensed
matter experiments.
