  We study the linearization of a class of thick K-branes, namely,
four-dimensional domain walls generated by a scalar field with particular
nonstandard kinetic terms. The master equations for linear perturbations are
derived from the point of view of both dynamical equations and quadratic
action. The spectra of the canonical normal modes are studied using
supersymmetric quantum mechanics. Our results indicate that the scalar
perturbation is nonlocalizable in general. Conditions for stable $K$-branes are
also found.
