  In this paper we propose the study of the photoproduction of charmoniumlike
states in $pp$ collisions at RHIC and LHC energies and estimate the rapidity
distribution and total cross sections for the production of the exotic hadrons
$Y(3940)$, $X(3915)$, $Z(4430)$ and $Z_c(3900)$. We demonstrate that the
experimental analysis of this process can provide complementary and independent
checks on these states, and help to understand their underlying nature.
