A hamster that keeps falling over is often suffering from a problem with its vestibular system. The vestibular system is the set of tissues within mammals that help us balance.
If your hamster also tilts its head to one side and wobbles as it walks, then it has likely got a problem somewhere within its ears, such as an infection or tumour. Ear infections can often be treated by a vet through a course of antibiotics, but if it’s a more serious problem, like a tumour, then the problem may be more difficult to treat. We recommend that you take your hamster to the vet for a diagnosis and treatment.

A hamster with an unsteady gait could be suffering from a problem with its ears
Another reason that your hamster could be a little unsteady on its feet is that it has recently suffered a stroke. If your hamster sways as it’s walking, tilts its head a lot, or walks in circles, then your hamster could’ve recently suffered a stroke. For more information on strokes, have a look at our hamster illnesses page.
Anna, 14 March 2022
My daughter's hamster hasn't been cleaning herself very well and there is a odor, it's not wet tail because it's been going on for about 2 wks now. We have been cleaning her ourselves every evening but now I've noticed her left front leg is swollen and she is very unsteady when she walks...Any suggestions or ideas of what may be going on??? She's a little over 2 yrs old....