  In this paper, we will prove that any $\A^3$-form over a field $k$ of
characteristic zero is trivial provided it has a locally nilpotent derivation
satisfying certain properties. We will also show that the result of T.
Kambayashi on the triviality of separable $\A^2$-forms over a field $k$ extends
to $\A^2$-forms over any one-dimensional Noetherian domain containing $\bQ$.
