We shall give the first and second $\alpha$-, $\beta$-, $\gamma$- and $f$-duals of the sets $c_0(\Lambda)$, $c(\Lambda)$ and $c_\infty(\Lambda)$ of sequences that are $\Lambda$-strongly convergent to naught, convergent and bounded. Furthermore, we shall determine the first and second continuous dual spaces of the sets $c_0(\Lambda)$ and $c(\Lambda)$.