The $D^{*}{\overline{D}}^{*}$ and $B^{*}{\overline{B}}^{*}$ systems are studied dynamically in the one boson exchange model, where $\pi$, $\eta$, $\sigma$, $\rho$ and $\omega$ exchanges are taken into account. Ten allowed states with low spin parity are considered. We suggest that the $1^{--}$, $2^{++}$, $0^{++}$ and $0^{-+}$ $B^{*}{\overline{B}}^{*}$ molecules should exist, and the $D^{*}{\overline{D}}^{*}$ bound states with the same quantum numbers very likely exist as well. However, the $CP$ exotic $(1^{-+},2^{+-})$ $B^{*}{\overline{B}}^{*}$ and $D^{*}{\overline{D}}^{*}$ states may not be bound by the one boson exchange potential. We find that the $I=0$ configuration is more deeply bound than the $I=1$ configuration, hence $Z_1^{+}(4050)$ may not be a $D^{*}{\overline{D}}^{*}$ molecule. Although $Y(4008)$ is close to the $D^{*}{\overline{D}}^{*}$ threshold, the interpretation of $Y(4008)$ as a $D^{*}{\overline{D}}^{*}$ molecule is not favored by its huge width. $1^{--}$ $D^{*}{\overline{D}}^{*}$ and $B^{*}{\overline{B}}^{*}$ states can be produced copiously in $e^{+}{e}^{-}$ annihilation, detailed scanning of the $e^{+}{e}^{-}$ annihilation data near the $D^{*}{\overline{D}}^{*}$ and $B^{*}{\overline{B}}^{*}$ threshold is an important check to our predictions.

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