This paper presents a pre-formal social cognitive model of social responsibility as implying the deliberative capacity of the bearer but not necessarily her decision to act or not. Also, responsibility is defined as an objective property of agents, which they cannot remit at their will. Two specific aspects are analysed: (a) the action of "counting upon" given agents as responsible entities, and (b) the consequent property of accountability: responsibility allows to identify the locus of accountability, that is, which agents are accountable for which events and to what extent. Agents responsible for certain events, and upon which others count, are asked to account or respond for these events. Two types of responsibility are distinguished and their commonalities pointed out: (a) a primary form of responsibility, which is a consequence of mere deliberative power, and (b) a task-based form, which is a consequence of task commitment. Primary responsibility is a relation between deliberative agents and social harms, whether these are intended and believed or not, and whether they are actually caused by the agent or not. The boundaries of responsibility will be investigated, and the conceptual links of responsibility with obligation and guilt will be examined. Task-based responsibility implies task- or role-commitment. Furthermore, individual Vs. shared Vs. collective responsibility are distinguished. Considerations about the potential benefits and utility of the analysis proposed for in the field of e-governance are highlighted. Concluding remarks and ideas for future works are discussed in the final section.