  We consider a generalisation of the self-affine iterated function systems of
Lalley and Gatzouras by allowing for a countable infinity of non-conformal
contractions. It is shown that the Hausdorff dimension of the limit set is
equal to the supremum of the dimensions of compactly supported ergodic
measures. In addition we consider the multifractal analysis for countable
families of potentials. We obtain a conditional variational principle for the
level sets.
