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The $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ systems are studied dynamicallyin the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and$\omega$ exchanges are taken into account. Ten allowed states with low spinparity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and$0^{-+}$ $B^{*}\bar{B}^{*}$ molecules should exist, and the $D^{*}\bar{D}^{*}$bound states with the same quantum numbers very likely exist as well. However,the CP exotic ($1^{-+}$, $2^{+-}$) $B^{*}\bar{B}^{*}$ and $D^{*}\bar{D}^{*}$states may not be bound by the one boson exchange potential. We find that theI=0 configuration is more deeply bound than the I=1 configuration, hence$Z^{+}_1(4050)$ may not be a $D^{*}\bar{D}^{*}$ molecule. Although Y(4008) isclose to the $D^{*}\bar{D}^{*}$ threshold, the interpretation of Y(4008) as a$D^{*}\bar{D}^{*}$ molecule is not favored by its huge width. $1^{--}$$D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ states can be produced copiously in$e^{+}e^{-}$ annihilation, detailed scanning of the $e^{+}e^{-}$ annihilationdata near the $D^{*}\bar{D}^{*}$ and $B^{*}\bar{B}^{*}$ threshold is animportant check to our predictions.

Bound States of the Heavy Flavor Vector Mesons and Y(4008) and $Z^{+}_1(4050)$