Our source sample consists of 10 well-known pre-stellar and protostellar objects representing different masses and evolutionary states, thus providing a complete view of the various types of objects encountered along the first phases of star formation. The data presented in this work were acquired with the IRAM 30-m telescope near Pico Veleta (Spain) and consist of unbiased spectral surveys at millimetre wavelengths. These are part of the Large Programme ASAI, whose observations and data reduction procedures will be presented in detail in an article by Lefloch & Bachiller (in preparation). Briefly, we gathered the spectral data in several observing runs between 2011 and 2014 using the EMIR receivers at 3 mm (80-116 GHz), 2 mm (129-173 GHz), and 1.3 mm (200-276 GHz). (13 data files).