The BRST cohomologies of non-critical massive string models are analysed in
detail in the range of dimensions 1 < d < 26. The classical theorems on va
nishing of Dolbeaut type and relative cohomologies are proved. The no-ghost
theorem is proved in the same range of dimensions. It is also shown that t
he BRST complex of the massive string model is a resolution of the non-crit
ical Nambu-Goto string in all spacetime dimensions 1 < d < 25.