  We propose a definition of nonclassicality for a single-mode quantum-optical
process based on its action on coherent states. If a quantum process transforms
a coherent state to a nonclassical state, it is verified to be nonclassical. To
identify nonclassical processes, we introduce a representation for quantum
processes, called the process-nonclassicality quasiprobability distribution,
whose negativities indicate nonclassicality of the process. Using this
distribution, we derive a relation for predicting nonclassicality of the output
states for a given input state. We experimentally demonstrate our method by
considering the single-photon addition as a nonclassical process, and
predicting nonclassicality of the output state for an input thermal state.
