Stellar feedback , expanding H ii regions , wind-blown bubbles , and supernovae are thought to be important triggering mechanisms of star formation . Stellar associations , being hosts of significant numbers of early-type stars , are the loci where these mechanisms act . In this part of our photometric study of the star-forming region NGC 346/N 66 in the Small Magellanic Cloud , we present evidence based on previous and recent detailed studies , that it hosts at least two different events of triggered star formation and we reveal the complexity of its recent star formation history . In our earlier studies of this region ( Papers I , III ) we find that besides the central part of N 66 , where the bright OB stellar content of the association NGC 346 is concentrated , an arc-like nebular feature , north of the association , hosts recent star formation . This feature is characterized by a high concentration of emission-line stars and Young Stellar Objects , as well as embedded sources seen as IR-emission peaks that coincide with young compact clusters of low-mass pre-main sequence stars . All these objects indicate that the northern arc of N 66 encompasses the most current star formation event in the region . We present evidence that this star formation is the product of a different mechanism than that in the general area of the association , and that it is triggered by a wind-driven expanding H ii region ( or bubble ) blown by a massive supernova progenitor , and possibly other bright stars , a few Myr ago . We propose a scenario according to which this mechanism triggered star formation away from the bar of N 66 , while in the bar of N 66 star formation is introduced by the photo-ionizing OB stars of the association itself .