Hi,
I am new to Ducati so sorry in advance if this is a stupid question. Giving the bike a once over, I came to the rear end and on checking the chain I found that the rear sprocket moves as if it were loose, I tighten or tried to tighten the nuts facing me on the sprocket but they were tight. Is this right or do I need to do so work on it first.
Thanks Eddie.
Welcome to the world of Cush-drive rubbers, aftermarket sprocket carriers, bushes and circlips.
Model and year information is useful, pictures even more so.
Cush drive rubbers can fail and are not too difficult to replace as long as you have a big socket (and bar) to take the centre nut off.
There should be enough slack in the chain to remove the sprocket and carrier intact if you turn the eccentric adjuster right to the front.
Thereafter it depends if you have a standard sprocket or an aftermarket carrier setup, the most common aftermarket ones are Talon and Renthal.
On earlier (Pre 99 ish) bikes the alloy centre that the sprocket is bolted to was a single piece and the sprocket was retained at the back by a large steel circlip sitting in a groove in the alloy centre and over a period of time the steel circlip wears away the alloy, the groove becomes wider and the sprocket can move towards and way from the swingarm.
Later alloy centres are not as deep and have a separate piece of harder material behind instead of the circlip, to prevent this problem, and some of the aftermarket sprocket carriers have various design features which, if they are badly worn, may be causing the movement you have.
Could be an easy fix, could cost a few quid, but you knew that when you bought a Ducati didn’t you? 
The rear sprocket carrier/cush drive on the 916 range was a bit of a lousy design. for all the reasons given in the previous post. I have seen pictures of swingarms with the whole chain adjuster worn off by the cush drives. When I bought the 996, one of the first preventative measures was to buy a renthal rear sprocket carrier to at least remove the dodgy cush drive issue from ever arising. The rear of the carrier has ridges that prevent the cush drive steel from moving towards the adjuster in case of failure. The circlip issue is another thing altogether. Here are 2 images of the old and new carrier anyway. Might be useful to somebody at a later date.
Renthal sprocket carrier showing the in built cush drive failure protection (we put a lot of trust in the rubber staying bonded to the metal surround of the cush drives. Well, some do, I bottled it and went Renthal. A lot easier to change rear sprockets with a renthal as well.
and heres that scary image where the cush drives murdered the chain adjuster on someone else bike
10 posts moderated before I can post freely. Its frustrating, so apologies up front for anyone who thinks I have posted a lot in the last couple of days. At least they should be useful posts.
The 10 post requirement helps us keep the forum quality high and keeps spammers out.
Not complaining. Was genuinely pointing out why as soon. As group of posts was modded it would look like I just carpet bombed the forum for anyone looking at new posts.