The near-cutoff propagation of free waves of flexure in a transversely isotropic, linearly electroelastic plate is studied, in two cases: for the simplest kinematics, when both the mechanical displacement and the electric potential are taken linear in the thickness variable; and for the entriched, third-order kinematics. The dispersion curves are four in the second case, only two in the first. By a comparison with the first four dispersion curves obtained by solving the corresponding three-dimensional problem, it is shown that perhaps the most definite advantage of adopting an enriched kinematics is a better approximation of the low-cutoff curves. (C) 2002 Elsevier Science B.V All rights reserved.