This study describes how Turkish and Moroccan adults acquire Dutch possessive clauses in which the verb have expresses the possessive relationship. The acquisition process is explained within the framework of recent generative theory in which have-clauses are assumed to be copular locative constructions. In this theory, predicate inversion of the locative PP and incorporation of the locative P0 into a be-copula are the main characteristics of a possessive have-clause. Assuming that all linguistic knowledge of the L1 is present, L2 learners rely on it from the earliest stages, irrespective of whether this L1 knowledge is parameter-related or not. The results confirm such a “conservation” viewpoint, which accounts for how the possessive relationship is expressed in the earliest stages and why these learners have their language-specific difficulties in discovering the target have-construction. The results corroborate the conservation effect of both parametrized linguistic knowledge, viz., the strong features triggering predicate inversion, and non-parametrized knowledge, viz., knowledge of syntax, morphology and morphological realization rules, and properties of lexical items.