  We study the triangular lattice bilayer Heisenberg model with
antiferromagnetic interplane coupling $J_\perp$ and nearest neighbour
intraplane coupling $J= \lambda J_\perp$, which can be ferro- or
antiferromagnetic, by expansions in $\lambda$. For negative $\lambda$ a phase
transition is found to an ordered phase at a critical $\lambda_c=-0.2636 \pm
0.0001$ which is in the 3D classical Heisenberg universality class. For
$\lambda>0$, we find a transition at a rather large $\lambda_c\approx 1.2$. The
universality class of the transition is consistent with that of Kawamura's 3D
antiferromagnetic stacked triangular lattice. The spectral weight for the
triplet excitations, at the ordering wavevector, remains finite at the
transition, suggesting that a phase with free spinons does not exist in this
model.
