In a mathematical model of the cellular immune response we investigate immune reactions to tumors that are introduced in various doses. The model represents macrophage T-lymphocyte interactions that generate cytotoxic macrophages and cytotoxic T-lymphocytes. In this model antigens (tumors) can induce infinitely large T-lymphocyte effector populations because effector T-lymphocytes are capable of repeated proliferation and we have omitted immunosuppression. In this (proliferative) model small doses of weakly antigenic tumors grow infinitely large (i.e. sneak through) eliciting an immune response of limited magnitude. Intermediate doses of the same tumor induce larger immune responses and are hence rejected. Large doses of the tumor break through, but their progressive growth is accompanied by a strong immune response involving extensive lymphocyte proliferation. Similarly a more antigenic tumor is rejected in intermediate doses and breaks through in large doses. Initially small doses however lead to tumor dormancy. Thus although the model is devoid of explicit regulatory mechanisms that limit the magnitude of its response (immunosuppression is such a mechanism), the immune response to large increasing tumors may either be a stable reaction of limited magnitude (experimentally known as tolerance or unresponsiveness) or a strong and ever increasing reaction. Unresponsiveness can evolve because in this model net T-lymphocyte proliferation requires the presence of a minimum number of helper T cells (i.e. a proliferation threshold). Unresponsiveness is caused by depletion of helper T cell precursors.