The ability to detect non-adjacent dependencies (NADs) in language--such as the dependency between the auxiliary 'is' and the present progressive marker '-ing' in 'the baker is baking bread'--could be extremely useful in language acquisition. It would provide the learner with information about which grammatical elements participate in the dependencies, and would also provide a cue to constituency and hierarchical structure. Yet published behavioral findings contain no evidence that children detect NADs before 15 months of age, and in particular, studies with 12-month-olds have failed to find evidence of learning. In the first part of the talk I will present evidence that even in adults, NAD learning is heavily influenced by subtle properties of the stimulus, such as rhythm and timing. I will then present new data that shows evidence of NAD learning in 12-month-old infants, when the artificial language stimuli are presented at speech rates that are faster than in past studies, and closer to natural speech. In the second part of the talk, I will discuss a new direction my lab is pursuing to explore the general capacity of NAD learning in the non-linguistic domain of human action sequences. I will present recent data showing that 9-month-olds learn non-adjacent repetition patterns (ABA rules) in human action sequences, as they do in speech, even though they have been shown to have difficulty with other visual stimuli. I will conclude by speculating that the learning successes in the domains of speech and human action might be the result of richer representations afforded to stimuli that are produced by human agents. If so, this could inform theories and research on infant language acquisition, and in particular research on NAD learning in infants.