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We construct with a geometric procedure the supersymmetry transformation lawsand Lagrangian for all the ``variant'' D=11 and D=10 Type IIA supergravities.We identify into our classification the D=11 and D=10 Type IIA ``variant''theories first introduced by Hull performing T-duality transformation on bothspacelike and timelike circles. We find in addition a set of D=10 Type IIA``variant'' supergravities that can not be obtained trivially from elevendimensions compactifying on a circle.Comment: 21 pages, Late

On the construction of variant supergravities inD= 11,D= 10