Following results were proved: 1. For any non-trivial action of (C, +) on the polynomial ring C[X,Y,Z] the ring of invariants C[X,Y,Z]Ga is isomorphic to a polynomial ring in two variables.

2. (Jointly with Avinash Sathaye) Let (C,+) act regularly and non-trivially on a smooth affine 3-fold X with trivial integral homology, Then the quotient X/(C,+) is smooth. The proof of (1) is much more accessible than the original proof of M. Miyanishi.