2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53331A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of quasisuperconformal and ${\bf Z}_2\times{\bf Z}_2$-graded algebras are obtained and in addition to the previously known cases five exceotional quasisuperconformal algebras and a series of ${\bf Z}_2\times{\bf Z}_2$-superconformal algebras containing affine $\widehat{sp}_2\otimes\widehat{osp}(N|2M)$ are constructed.11 pages, ITP-SB-92-34, LatexHigh Energy Physics - Theorytext