We present William Herschel Telescope (WHT) and Very Large Telescope (VLT) spectroscopy of MM Ser, the optical counterpart to Ser X-1. We deblend the red spectra of the two close stars identified by Wachter and show that the brighter of the two is responsible for the Hα and He I emission, hence confirming that this is the true counterpart of the X-ray source. We also identify several HeII and NIII lines in the blue spectrum. The isolated emission lines are all remarkably narrow, with FWHM 200-300 km s-1. The Bowen blend has structure suggesting that the individual components are also narrow. These narrow lines could be from the disc if the binary inclination is quite low, or they could come from a more localized region such as the heated face of the companion star. Several interstellar lines are detected and indicate that the reddening is moderate, and consistent with the neutral hydrogen column density inferred in X-rays.