  We classify the singularities of a surface ruled by conics: they are rational
double points of type $A_n$ or $D_n$. This is proved by showing that they arise
from a precise series of blow-ups of a suitable surface geometrically ruled by
conics. We determine also the family of such surfaces which are birational
models of a given surface ruled by conics and obtained in a "minimal way" from
it.
