  We study a class of noncanonical real scalar field models in
$(1+1)$-dimensional flat space-time. We first derive the general criterion for
the classical linear stability of an arbitrary static soliton solution of these
models. Then we construct first-order formalisms for some typical models and
derive the corresponding kink solutions. The linear structures of these
solutions are also qualitatively analyzed and compared with the canonical kink
solutions.
