Dogs were trained (by rewarding correct choices and refusing reward at incorrect ones) to obtain food by lifting a bar when presented with the correct auditory stimulus. Two buzzers of different frequency characteristics were employed as stimuli, and one animal each was trained to each of the following problems: (a) respond to H(high frequency) buzzer, not to L(low frequency); (b) respond to HL simultaneously, but not to respond to either alone; (c) respond to H or L singly but not to both presented simultaneously; (d) respond to H followed by L, but not to respond to H,H, (successively) or L,L; (e) respond to either H,H, or L,L, but not to H,L. All problems were learned[long dash]i.e., the response was consistently made to rewarded stimulus while response to unrewarded stimuli dropped out[long dash]in from 700-1400 trials. Results bear out theoretical predictions that discriminations between two stimuli are easier than between either and a composite of both, and that extinction of a habit of response to a compound stimulus when components are reinforced (problem b above) is more difficult than extinction of the converse habit (c above). It is pointed out that in view of the complexity of the "conditioned stimulus," the search for laws of compound conditioning constitutes a search for principles to deal with situations under which learning occurs. The findings are discussed in the light of theoretical positions of Pavlov and of Hull.