ALLSMOG is an ESO Large Programme for the Atacama Pathfinder EXperiment (APEX, project no.: E-192.A-0359, principal investigator (PI): J. Wagg) targeting the CO(2-1) emission line (rest frequency, ν_CO(2-1)=230.538GHz) in 88 local, low-M* star-forming galaxies. The project was initially allocated 300h of ESO observing time over the course of four semesters, corresponding to 75h per semester throughout periods P92-P95 (October 2013 - September 2015). However, during P94 and P95 there was a slowdown in ALLSMOG observations, mainly due the installation of the visiting instrument Supercam in combination with better-than-average weather conditions - causing other programmes requiring more stringent precipitable water vapour (PWV) constraints to be prioritised. Because of the resulting ~50% time loss for ALLSMOG during two semesters, the ESO observing programmes committee (OPC) granted a one-semester extension of the project, hence allowing us to complete the survey in P96 (March 2016). The final total APEX observing time dedicated to ALLSMOG amounts to 327h, including the overheads due to setup and calibration but not accounting for possible additional time lost because of technical issues. <P />In 2014 a northern component of the ALLSMOG survey was approved at the IRAM 30m telescope (project code: 188-14, PI: S. Martin), aimed at observing the CO(1-0) (rest frequency, ν<SUB>CO(1-0)</SUB>=115.271GHz) and CO(2-1) emission lines in a sample of nine additional galaxies characterised by stellar masses, M*<10<SUP>9</SUP>M<SUB>ȯ</SUB>. A total of 22h of observations were obtained with the IRAM 30m during two observing runs in November 2014 and May 2015. <P />(5 data files). <P />