  Starting from Wilson's action, we calculate strong coupling series for the
Polyakov loop susceptibility in lattice gauge theories for various small N_\tau
in the thermodynamic limit. Analysing the series with Pad\'e approximants, we
estimate critical couplings and exponents for the deconfinement phase
transition. For SU(2) pure gauge theory our results agree with those from
Monte-Carlo simulations within errors, which for the coarser N_\tau=1,2
lattices are at the percent level. For QCD we include dynamical fermions via a
hopping parameter expansion. On a N_\tau=1 lattice with N_f=1,2,3, we locate
the second order critical point where the deconfinement transition turns into a
crossover. We furthermore determine the behaviour of the critical parameters
with finite chemical potential and find the first order region to shrink with
growing \mu. Our series moreover correctly reflects the known Z(N) transition
at imaginary chemical potential.
