In this paper Stone-type theorems on existence of truth filters in De Morgan lattices are obtained. It is shown that $(^*)\cdots(a\wedge T)\cap T_0=\emptyset$ is necessary and sufficient for existence of a truth filter containing {\bf a}, where $T_0$ and $T_1$ are sets of zeroes and units. Also, it is proved that the filter $F$ is contained in a truth filter iff for each member {\bf a} of $F$ holds $(^*)$. Some other related results are proved, too.