Recently, considerable interest and research effort has been given to the problem of finding a suitable extension of the {\em logic programming paradigm} beyond the class of normal logic programs. In order to demonstrate that a class of programs can be justifiably called an {\em extension of logic programs} one should be able to argue that: \begin{itemize} \item the proposed {\em syntax} of such programs resembles the syntax of logic programs but it applies to a significantly broader class of programs; \item the proposed {\em semantics} of such programs constitutes an intuitively natural extension of the semantics of normal logic programs; \item there exists a reasonably simple procedural mechanism allowing, at least in principle, to compute the semantics; \item the proposed class of programs and their semantics is a special case of a more general non-monotonic formalism which clearly links it to other well-established non-monotonic formalisms. \end{itemize} In this paper we propose a specific class of extended logic programs which will be (modestly) called {\em super logic programs} or just \em {super-programs}. We will argue that the class of super-programs satisfies all of the above conditions, and, in addition, is sufficiently flexible to allow various application-dependent extensions and modifications. We also provide a brief description of a Prolog implementation of a {\em query-answering interpreter} for the class of super-programs which is available via FTP and WWW.