Three experiments investigating how two groups of adult Polish learners of Danish as a foreign language acquire the Danish dative alternation are reported. Experiment 1 is a speeded acceptability judgment task, which shows that Group 1 has the same pattern as native speakers i.e. slower responses to the dispreffered new-given NP-constructions, but no givenness effect with the PP-constructions. Experiment 2 shows that Group 2 also have acquired this pattern, even though earlier research suggests that the givenness asymmetry in the dative alternation is hard to learn. Experiment 3 shows that even in Polish there is a givenness asymmetry, such that the given–new order is clearly preferred in the NP-construction, but less so in the PP-construction. The rapid acquisition of the Danish pattern could thus be explained by Polish having the same pattern. In short: Both Polish and Danish have a givenness asymmetry in the dative alternation, which could explain why Polish learners of Danish in both groups behave almost like native Danish speakers.