The concept of quasi-hereditary algebras had been introduced in order to study the ring structure of blocks of the BGG-category \(\mathcal O\) of a finite dimensional semisimple complex Lie algebra. In a recent generalisation of \(\mathcal O\) [see \textit{V. Futorny, S. König, V. Mazorchuk}, J. Algebra 231, No. 1, 86-103 (2000; Zbl 1018.17004), Manuscr. Math. 102, No. 4, 487-503 (2000; Zbl 1018.17005), and another paper by the same authors, `Categories of induced modules and standardly stratified algebras', Algebr. Represent. Theory (to appear)] a more general class of algebras has emerged. Such `properly stratified' algebras are studied in the present paper from an abstract point of view. The definition requires the regular module to have two filtrations, one by `proper standard' modules (which are analogues of Verma modules), and another one by `standard' modules (whose simple top may occur again as a composition factor of the radical). An equivalent definition is given in terms of vanishing of second cohomology groups. These algebras are special examples of `stratified algebras' [see \textit{E. Cline, B. Parshall, L. Scott}, Mem. Am. Math. Soc. 591 (1996; Zbl 0888.16006) and \textit{I. Ágoston, V. Dlab, E. Lukács}, C. R. Math. Acad. Sci., Soc. R. Can. 20, No. 1, 22-28 (1998; Zbl 0914.16010)].