  We study the frustrated Heisenberg model on the bilayer honeycomb lattice.
The ground-state energy and spin gap are calculated, using different bosonic
representations at mean field level and numerical calculations, to explore
different sectors of the phase diagram. In particular we make use of a bond
operator formalism and series expansion calculations to study the extent of
dimer inter-layer phase. On the other hand we use the Schwinger boson method
and exact diagonalization on small systems to analyze the evolution of on-layer
phases. In this case we specifically observe a phase that presents a spin gap
and short range Neel correlations that survives even in the presence of
non-zero next-nearest-neighbor interaction and inter-layer coupling.
