Abstract:  In this paper we show that the $k$-total domination and signed total domination problems are NP-complete on doubly chordal graphs. Also, we present an unified approach to slove the signed total domination, minus total domination, $k$-total domination and $\{k\}$-total domination problems on a strongly chordal graph in linear-time, if the strong elemination ordering for the strongly chordal graph is given.