We are carrying out a programme of CO and interferometric H I observations in the nearby galaxy cluster Abell 1367. The aim is to better understand the processes driving the evolution of the ISM in late-type galaxies in the cluster environment. Abell 1367 is a dynamically young cluster. We have determined the H I content and g - i colour from AGES (Cortese 2008) and SDSS, respectively, of its bright late-type galaxies (spirals) in a volume centred on the NW subcluster. We use a combination of these characteristics, both of which are indicative of evolutionary history, to classify each spiral into one of four evolutionary states. This analysis revealed the cluster contains spirals in a wide range of evolutionary states. VLA D-array imaging centred on the NW subcluster indicates most galaxies in that field have their H I intensity maximum offset relative to its optical counterpart, implying a recent and strong disturbance. The direction of this offset is not always consistent with a simple scenario of ram pressure stripping by the cluster's high density intra-cluster medium (ICM).