  We define and describe simple complex Lie superalgbras of vector fields on
"supercircles" - simple stringy superalgebras. There are four series of such
algebras and four exceptional stringy superalgebras. The 13 of the simple
stringy Lie superalgebras are distinguished: only they have nontrivial central
extensions; since two of the distinguish algebras have 3 nontrivial central
extensions each, there are exactly 16 superizations of the Liouville action,
Schroedinger equation, KdV hierarchy, etc. We also present the three nontrivial
cocycles on the N=4 extended Neveu-Schwarz and Ramond superalgebras in terms of
primary fields and describe the "classical" stringy superalgebras close to the
simple ones. One of these stringy superalgebras is a Kac-Moody superalgebra
G(A) with a nonsymmetrizable Cartan matrix A. Unlike the Kac-Moody
superalgebras of polynomial growth with symmetrizable Cartan matrix, it can not
be interpreted as a central extension of a twisted loop algebra.The stringy
superalgebras are often referred to as superconformal ones. We discuss how
superconformal stringy superalgebras really are.
