A necessary and sufficient geometric condition is established for the Kohn Laplacian to be hypoelliptic, modulo its
nullspace, for boundaries of arbitrary infinitely differentiable pseudoconvex tube domains in two complex variables.
Hypoellipticity is also proved to be equivalent to validity of a superlogarithmic estimate, for this special class of
structures.
AMS 2000 Mathematics subject classification: Primary 32W05; 32T27. Secondary 35J70.