Vomiting and diarrhoea are not unusual in cats, however since most cats have access to the outdoors, diarrhoea in particular may not be recognised easily by owners. Both vomiting and diarrhoea are symptoms of other conditions rather than diseases in their own right and there is a vast range of diseases in which diarrhoea and/or vomiting may occur. In many cases the problem may be successfully treated without ever pinpointing the actual cause. However, the information that you give your vet may be vital in deciding whether the case is serious enough to need further detailed investigations.
Both diarrhoea and vomiting occur as short lived (acute) conditions lasting 1-2 days which will often clear up on their own, and as long-term (chronic) problems which may be more serious. If your cat has vomiting or diarrhoea but does not appear to be in distress or be losing weight, all you may need to do is to withhold all food for a day and then give your cat small amounts of cooked fish, chicken or some other food which is easily digested. Make sure clean fresh water is available. If the problem persists or stops but then recurs you should make an appointment to see your vet.
Constipation is also not unusual in cats. Long term constipation can make cats feel miserable and they may stop eating. If you notice your cat spending time in the litter tray but not passing anything (or if your cat is producing small hard faecal pellets) then you should take a trip to the vets. Some urinary tract problems such as cystitis or urinary tract blockage can also be mistaken for constipation so it is important to get an accurate diagnosis.