This paper reviews the rise of geographic concentrations of small food-processing units in rural areas of Latin America, in order to show that, drawing on the literature on the development of clusters, they may represent a type of local productive system, namely Local Agri-food Systems. Furthermore it assesses whether they might compete efficiently in global food commodity chains. In this regard it analyses the specific assets of these systems, drawing on some specific cases, and stresses the conditions that can enable them to compete on national or even global markets in the supply of processed products. These conditions appear to be a capacity for collective action which, in this particular case, will be enhanced by qualification processes of the products creating common assets for the actors involved. These elements could provide a rationale as regards the categorization of clusters according to their efficiency. Actually, although they won't be able to achieve competitive efficiency in every case, some might, and it remains useful to set up a research programme on their trajectories of development.