  Magnetic properties of a mixed spin-1/2 and spin-1 Ising model on honeycomb
lattice are exactly investigated within the framework of generalized
star-triangle mapping transformation. The particular attention is focused on
the effect of uniaxial and biaxial crystal-field anisotropies that basically
influence the magnetic behaviour of the spin-1 atoms. Our results for the basic
thermodynamic quantities, as well as the dynamical time-dependent
autocorrelation function indicate the spin tunneling between the $| +1>$ and $|
- 1>$ states in the magnetically ordered phase.
