Abstract: We consider the holomorphic extension of CR functions from certain hypersurfaces with singularity. It is proved that CR functions on a quadratic cone M in Cⁿ, n>1, admit one-sided holomorphic extension if and only if M does not have two-sided support, a geometric condition on M which generalizes minimality in the sense of Tumanov. A biholomorphic classification of quadratic cones in C² is also given.