  We consider the extended superconformal algebras of the Knizhnik-Bershadsky
type with $W$-algebra like composite operators occurring in the commutation
relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2,
only. These have recently been neatly classified by several groups, and we
emphasize the classification based on hamiltonian reduction of affine Lie
superalgebras with even subalgebras $G\oplus sl(2)$. We reveiw the situation
and improve on previous formulations by presenting generic and very compact
expressions valid for all algebras, classical and quantum. Similarly generic
and compact free field realizations are presented as are corresponding
screening charges. Based on these a discussion of singular vectors is
presented. (Based on talk by J.L. Petersen at the Int. Workshop on "String
Theory, Quantum Gravity and the Unification of the Fundamental Interactions",
Rome Sep. 21-26, 1992)

High Energy Physics - Theory