It is possible for the tiny components of mechanical wrist watches to become magnetised when placed in closed proximity to strong magnetic fields if the parts are made from ferrous material. 

If the mechanical ferrous parts become magnetised, they can attract each other or attract to the inside of the casing causing the watch to run fast or slow, or cease working altogether.

Many modern watches are now made from ‘non-magnetic’ material and therefore are resistant to fairly weak magnetic fields. 

To be on the safe side, you should always keep your mechanical watch away from strong magnetic fields. 

If your watch does become magnetised, a watch repair shop should be able to demagnetise it and return it to its correct operation.