If the director does not concur with the secretary's choice, then the secretary is required to notify the president of the director's nonconcurrence.

The Senate acted in a show of hands on a so-called nonconcurrence resolution, a motion to reject the treaty.

All is not supine nonconcurrence.

Concurrence is the noun, its opposite nonconcurrence; what is wrong with taking another step into a verb like nonconcur?

"It may be worthwhile to apply Department of Energy resources to concentrate on the Iraq issue," Mr. Walsh wrote in a letter of nonconcurrence.