We present a spectroscopic study of the N159/N160 massive-star forming region south of 30 Doradus in the Large Magellanic Cloud, classifying a total of 189 stars in the field of the complex. Most of them belong to O and early B spectral classes; we have also found some uncommon and very interesting spectra, including members of the Onfp class, a Be P Cygni star, and some possible multiple systems. Using spectral types as broad indicators of evolutionary stages, we considered the evolutionary status of the region as a whole. We infer that massive stars at different evolutionary stages are present throughout the region, favoring the idea of a common time for the origin of recent star formation in the N159/N160 complex as a whole, while sequential star formation at different rates is probably present in several subregions.