The reconstruction conjecture for posets is the following : every finite poset P of more than three elements is uniquely determined - up to isomorphism - by its collection of (unlabelled) one-element-deleted subposets [ P - {x} : x V (P) ]. This conjecture belongs to the list of open problems in Order. We show that disconnected posets, posets with unique minimal (respectively, maximal) element and interval orders are reconstructible and that N-free orders are recognizable. We show that the following parameters are reconstructible : the number of minimal (respectively, maximal) elements, the level structure, the ideal-size sequence of the maximal elements, the ideal size (respectively, filter-size) sequence of any fixed level of the HASSE-diagram and the number of edges of the HASSE-diagram. This is considered to be a first step towards a proof of the reconstruction conjecture for posets.