  We derive a duality-symmetric action for type IIA D=10 supergravity by the
Kaluza-Klein dimensional reduction of the duality-symmetric action for D=11
supergravity with the 3-form and 6-form gauge field. We then double the bosonic
fields arising as a result of the Kaluza-Klein dimensional reduction and add
mass terms to embrace the Romans's version, so that in its final form the
bosonic part of the action contains the dilaton, NS-NS and RR potentials of the
standard type IIA supergravity as well as their duals, the corresponding
duality relations are deduced directly from the action. We discuss the relation
of our approach to the doubled field formalism by Cremmer, Julia, Lu and Pope,
complete the extension of this construction to the supersymmetric case and lift
it onto the level of the proper duality-symmetric action. We also find a new
dual formulation of type IIA D=10 supergravity in which the NS-NS two-form
potential is replaced with its six-form counterpart. A truncation of this dual
model produces the Chamseddine's version of N=1, D=10 supergravity.
