  We study the strong decay channels $P_c^+(4380) \to J/\psi p$ and
$P_c^+(4450) \to J/\psi p$ under $\Sigma_c \bar{D}^*$ molecular state ansatz.
With various spin-parity assignments, the partial decay widths of $J/\psi p$
final state are calculated. Our results show that all the $P$ wave $\Sigma_c
{\bar D}^*$ assignments are excluded, while $S$ wave $\Sigma_c {\bar D}^*$
pictures for $P_c(4380)$ and $P_c(4450)$ are both allowed by present
experimental data. The $J^P=3/2^-$ $\Sigma_c^* \bar{D}$ and $\Sigma_c^*
\bar{D}^*$ molecules are also discussed in the heavy quark limit, and find that
the $\Sigma_c^* \bar{D}$ system for $P_c(4380)$ is possible. More experimental
information on spin-parities and partial decay widths and theoretical
investigations on other decay modes are needed to clarify the nature of the two
$P_c$ states.
