Abstract: The recently discovered P-c(4380)(+) and P-c(4450)(+) states at LHCb have masses close to the (D) over bar Sigma(C)* and (D) over bar*Sigma(C) thresholds, respectively, which suggest that they may have significant meson-baryon molecular components. We analyze these states in the framework of a constituent quark model which has been applied to a wide range of hadronic observables, being the model parameters, therefore, completely constrained. The P-c(4380)(+) and P-c(4450)(+) are studied as molecular states composed by charmed baryons and open charm mesons. Several bound states with the proper binding energy are found in the (D) over bar Sigma(C)* and (D) over bar*Sigma(C) chennels. We discuss the possible assignments of these states from their decay widths. Moreover, two more states are predicted, associated with the (D) over bar Sigma(C) and (D) over bar*Sigma*(C) thresholds. (C) 2016 Published by Elsevier B.V.