Different formulations of chiral bosons

It is shown, that recently constructed PST Lagrangians for chiral supergrav ities follow directly from earlier Kavalov-Mkrtchyan Lagrangians by an Ansa tz for the theta tensor by expressing this in terms of the PST scalar. The susy algebra which included earlier alpha-symmetry in the commutator of sup ersymmetry transformations, is now shown to include both PST symmetries, wh ich arise from the single cu-symmetry term. The Lagrangian fur the 5-brane is not described by this correspondence, and probably can be obtained from more general Lagrangians, possessing alpha-symmetry. (C) 1999 Published by Elsevier Science B.V. All rights reserved.