This paper examines whether the acquisition of word order is subject to transfer in child second language learners (cL2), as has been claimed for adult second language learners (cf. the Full Transfer Full Access Hypothesis (FTFA), Schwartz and Sprouse 1996). Specifically, the acquisition of V2-placement and the Head-Direction Parameter (Neeleman and Weerman 1999) is analysed in two groups of cL2 learners with first exposure to their L2 between the ages of 3 and 4: 24 children have German as L1 and acquire French as an L2; 11 children have French as L1, acquiring German as an L2. The results show an unexpected asymmetry in the occurrence of transfer depending on which language represents the L1: (1) L1-German children acquiring French exhibit correct placement of the subject in French and no transfer of V2, whereas L1-French children acquiring German use (incorrect) V3 constructions in German; (2) in sentences with complex verb groups, both groups of children produce the wrong pattern (non target-like) VO-patterns in German and (non target-like) OV-patterns in French. The observed asymmetry challenges the Full Transfer Full Access Hypothesis, in that the cross-linguistic influence seems to depend on structural properties of the languages involved, rather than reflecting full transfer from any L1 to L2. Moreover the attested transfer does not appear at the onset of the acquisition but only later, contrary to the prediction of the FTFA.