This study tests the hypothesis that developmental dyslexia is (partly) caused by a deficit in implicit sequential learning, by investigating whether infants at familial risk of dyslexia can track non-adjacent dependencies in an artificial language. An implicit learning deficit would hinder detection of such dependencies, which mark grammatical relations (e.g. between "is" and "-ing" in "she is happily singing"). In a head-turn experiment with infants aged 1;6, family risk and typically developing infants were exposed to one of two novel languages containing dependencies of the type a-X-c, b-X-d or a-X-d, b-X-c, with fixed first and third elements and twenty-four different X elements. During test, typically developing children listened longer to ungrammatical strings (i.e. that did not correspond to their training language). However, family-risk children did not discriminate between grammatical and ungrammatical strings, indicating deficient implicit learning. The implications of these findings in relation to dyslexia and other language-based disorders are discussed.