On compactification of a Clemens family of three-dimensional algebraic varieties

We study some families of projective threefolds having the conic-bundle over $\mathbf{P^2}$ with the non-ample anticanonical class as a generic fiber. Using some recent fundamental results of Sh. Mori we prove that each fiber of such a family has the structure of a conic-bundle over $\mathbf{P^2}$. We give a negative answer to a question raised by С. H. Clemens in 1974 on the existence of a smooth compactification of the special family.