Abstract
We investigate smooth affine surfaces with G m -actions and A ∗ 1 -fibrations. We consider a smooth affine surface with an untwisted A ∗ 1 -fibration over the affine line, and obtain a characterization of the fibration is unique in terms of the boundary divisor of the surface. As an application of the characterization, we know that a smooth affine surface admitting two independent G m -actions is isomorphic to A ∗ 1 × A ∗ 1 or A 1 × A ∗ 1 unless S has an A 1 -fibration over A 1 .
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