  The aim of this paper is to discus the relations between various notions of
sequential completeness and the corresponding notions of completeness by nets
or by filters in the setting of quasi-metric spaces. We propose a new
definition of right $K$-Cauchy net in a quasi-metric space for which the
corresponding completeness is equivalent to the sequential completeness. In
this way we complete some results of R.~A. Stoltenberg, Proc. London Math. Soc.
\textbf{17} (1967), 226--240, and V.~Gregori and J.~Ferrer, Proc. Lond. Math.
Soc., III Ser., \textbf{49} (1984), 36.
