  The purpose of this article is twofold. First of all, the notion of $(D,
E)$-quasi basis is introduced for a pair $(D, E)$ of dense subspaces of Hilbert
spaces. This consists of two biorthogonal sequences $\{ \varphi_n \}$ and $\{
\psi_n \}$ such that $\sum_{n=0}^\infty
\ip{x}{\varphi_n}\ip{\psi_n}{y}=\ip{x}{y}$ for all $x \in D$ and $y \in E$.
Secondly, it is shown that if biorthogonal sequences $\{ \varphi_n \}$ and $\{
\psi_n \}$ form a $(D ,E)$-quasi basis, then they are generalized Riesz
systems. The latter play an interesting role for the construction of
non-self-adjoint Hamiltonians and other physically relevant operators.
