  We discuss the heavy quark spin structure of the recently observed `twin'
resonances $Z_b(10610)$ and $Z_b(10650)$ assuming that these are mostly of a
`molecular' type, i.e. that their internal dynamics is dominated by the
coupling to meson pairs $B^* \bar B - B {\bar B}^*$ and $B^* {\bar B}^*$. We
find that the state of the $b \bar b$ pair within the $Z_b(10610)$ and
$Z_b(10650)$ resonances is a mixture of a spin-triplet and a spin-singlet of
equal amplitude and with the phase orthogonal between the two resonances. Such
a structure gives rise to specific relations between observable amplitudes that
are in agreement with the data obtained recently by Belle. We also briefly
discuss possible properties of the isotopically singlet counterparts of the
newly found resonances, and also of their $C$ ($G$) parity opposites that
likely exist in the same mass range near the open $B$ flavor threshold.
