Chinese elms are very susceptible to a leaf spot caused by the fungus Stegophora ulmea. But the only way to be 100% sure of the diagnosis is to have the leaf checked in plant pathology laboratory where they can isolate the fungus and identify it.
In any case if the symptoms are similar to the ones shown in this reference :
http://www.oznet.ksu.edu/path-ext/f...Elm%20Trees.asp you just have to follow the control measures they give to get rid of this disease.
Best of luck,
Alain.