Okay, fine, so maybe there are a few bikes without serial numbers, but this is rare and typical only on hand made bikes or really old bicycles. You can tell which Mark you have by the serial number. A prefix of 5 positions and a refference number of 6 positions. Example: GN72A 123725 GSX600FS 1995 : From 1995 it will gradually pass over to a VIN Number of 17 positions.
Frame number check is in most cases the same as VIN number check, for the vehicle identification number located on the frame is the primary number used to identify the vehicle - a car, a motorcycle, a truck or a trailer or even a bike. I have just dragged by old BSA Meteor out of the loft and it would appear to be a Mk 1 from from BSA Shaun's post.
