  In this paper, we investigate thick branes with a nonminimally coupled
background scalar field, whose solution is a single-kink or a double-kink. The
effects of the nonminimal coupling constant $\xi$ on the structure of the thick
branes and the localization of gravity, fermions, scalars and vectors are
discussed. It is shown that each brane will split into two sub-branes as
increasing the nonminimal coupling constant $\xi$. By investigating the tensor
perturbation equations of gravity and the general covariant Dirac equation of
fermions, we find that both the gravity zero mode and left-chiral fermion zero
mode are localized at the center of the single-kink branes and localized
between the two sub-branes generated by the double-kink, which indicates that
the constant $\xi$ does not effect the localization of these zero modes.
However, the zero mode of scalars is localized on each sub-brane (for both
single-kink and double-kink branes) when $\xi$ is larger than its critical
value $\xi_0$. The effects of the nonminimal coupling constant $\xi$ on the
resonances of gravity and fermions with finite lifetime on the branes are also
discussed.
