Let2F1(a,b;c;z) and Φ(a;c;z) denote the Gaussian hypergeometric function and confluent hypergeometric function respectively. It is well known that iffis univalent in the unit disc δ then the corresponding Alexander transform off, namelydt, is not necessarily univalent in the whole of δ In this paper we determine conditions on the parametersa,bandcso that the Alexander transform, wheref(z)=z2F1(a,b;c;z) or zΦ(a;c;z) is univalent and starlike in the whole of δ. In particular, we obtain conditions ona,b,cto guarantee that2F1(a,b;c;z) (and Φ(a;c;z) resp.) will be univalent in the whole of the unit disc.