N-free posets as generalizations of series-parallel posets

N-free posets have recently taken some importance and motivated many studies. This class of posets introduced by Grillet [8] and Heuchenne [11] are very related to another important class of posets, namely the series-parallel posets, introduced by Lawler [12] and studied by Valdes et al. [21]. This paper shows how N-free posets can be considered as generalizations of series-parallel posets, by giving a recursive construction of N-free posers. Furthermore we propose a linear time algorithm to recognize and decompose any N-free poset. This yields some very naturel problems, namely: which are the properties (such as linear time algorithm for some invariant) of seriesparallel posets that are kept for N-free posets?