  We present the detection of the free radicals NC$_3$S and HC$_3$S towards
TMC-1 with the QUIJOTE line survey. The derived column densities are
(1.4$\pm$0.2)$\times$10$^{11}$ for NC$_3$S and (1.5$\pm$0.2)$\times$10$^{11}$
for HC$_3$S. We searched for NCCS, but only three transitions are within the
domain of our QUIJOTE line survey and the observed lines are marginally
detected at the 3$\sigma$ level, providing an upper limit to its column density
of $\leq$6$\times$10$^{10}$ cm$^{-2}$. We also unsuccessfully searched for
longer species of the NC$_n$S (n$\ge$4) and HC$_n$S (n$\ge$5) families in our
TMC-1 data. A chemical model based on a reduced set of reactions involving
HC$_3$S and NC$_3$S predicts abundances that are 10-100 times below the
observed values. These calculations indicate that the most efficient reactions
of formation of HC$_3$S and NC$_3$S in the model are S + C$_3$H$_2$ and N +
HC$_3$S, respectively, while both radicals are very efficiently destroyed
through reactions with neutral atoms.
