We give necessary and sufficient conditions for a few classes of circulant
graphs/digraphs to be singular. We also give two generalizations of the above
graphs/digraphs, namely $(r,s,t)$-digraphs for non-negative integers $r,s$ and
$t$, and the digraph $C_n^{i,j,k,l}$ with certain restrictions. A necessary and
sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular is
obtained. Some necessary conditions are given under which the
$(r,s,t)$-digraphs are singular.