  A list of superconformal chiral operator product expansion algebras with
quadratic nonlinearity in two dimensions is completed on the basis of the known
classification of little conformal Lie superalgebras. In addition to the
previously known cases and the constructed in our previous paper exceptional
$N=8$ superalgebra associated with $F(4)$, a novel exceptional $N=7$
superconformal algebra associated with $G(3)$ is found, as well as a whole
family of superalgebras containing affine $\widehat{su}_2 \oplus
\widehat{usp}_{2N}$. A classification scheme for quasisuperconformal algebras
is also outlined.
