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In this work, we have investigated whether Y(4260) and ${\rm Z^{+}_2(4250)}$could be ${\rm D_1D}$ or ${\rm D_0D^{*}}$ molecules in the framework of mesonexchange model. The off-diagonal interaction induced by $\pi$ exchange plays adominant role. The $\sigma$ exchange has been taken into account, which leadsto diagonal interaction. The contribution of $\sigma$ exchange is not favorableto the formation of molecular state ${\rm with I^{G}(J^{PC})=0^{-}(1^{--})}$,however, it is beneficial to the binding of molecule ${\rm withI^{G}(J^{P})=1^{-}(1^{-})}$. Light vector meson exchange leads to diagonalinteraction as well. For ${\rm Z^{+}_2(4250)}$, the contribution from $\rho$and $\omega$ exchange almost cancels each other. For the currently allowedvalues of the effective coupling constants and a reasonable cutoff $\Lambda$ inthe range 1-2 GeV, We find that Y(4260) could be accommodated as a ${\rm D_1D}$and ${\rm D_0D^{*}}$ molecule, whereas the interpretation of ${\rmZ^{+}_2(4250)}$ as a ${\rm D_1D}$ or ${\rm D_0D^{*}}$ molecule is disfavored.The bottom analog of Y(4260) and ${\rm Z^{+}_2(4250)}$ may exist, and the mostpromising channels to discovery them are $\pi^{+}\pi^{-}\Upsilon$ and$\pi^{+}\chi_{b1}$ respectively.

Are Y(4260) and {\rm Z$_2^{+}$(4250)} ${\rm D_1D}$ or ${\rm D_0D^{*}}$ Hadronic Molecules?