  We study a class of semilinear elliptic equations on spaces of tempered
ultradistributions of Beurling and Roumieu type. Assuming that the linear part
of the equation is an elliptic pseudodifferential operator of infinite order
with a sub-exponential growth of its symbol and that the non linear part is
given by an infinite sum of powers of $u$ with sub-exponential growth with
respect to $u,$ we prove a regularity result in the functional setting of the
quoted ultradistribution spaces for a weak Sobolev type solution $u$.
