There is a critical shortage of deceased human donor organs for transplantation. The need is perhaps most acute in neonates and infants with life-threatening congenital heart disease, in whom mechanical support devices are largely unsuccessful. If orthotopic (life-supporting) heart transplantation (OHTx) were consistently successful in the genetically engineered pig-to-nonhuman primate (NHP) model, a clinical trial of bridging with a pig heart in such patients might be justified. However, the results of pig OHTx in NHPs have been mixed and largely poor. We hypothesise that a factor is the detrimental effects of the inflammatory response that is known to develop (a) during any surgical procedure that requires cardiopulmonary bypass, and (b) immediately after an NHP recipient is exposed to a pig xenograft. We suggest that the combination of these two inflammatory responses has a direct detrimental effect on pig heart graft function, but also, and possibly of more importance, on recipient baboon pulmonary function, which further impacts survival of the pig heart graft. In addition, the inflammatory response almost certainly adversely impacts the immune response to the graft. If our hypothesis is correct, the potential steps that could be taken to reduce the inflammatory response or its effects (with varying degrees of efficacy) include (a) white blood cell filtration, (b) complement depletion or inactivation, (c) immunosuppressive therapy, (d) high-dose corticosteroid therapy, (e) cytokine/chemokine-targeted therapy, (f) ultrafiltration or CytoSorb hemoperfusion, (g) reduction in the levels of endogenous catecholamines, (h) triiodothyronine therapy and (i) genetic engineering of the organ-source pig. Prevention of the inflammatory response, or attenuation of its effects, by judicious anti-inflammatory therapy may contribute not only to early survival of the recipient of a genetically engineered pig OHTx, but also to improved long-term pig heart graft survival. This would open the possibility of initiating a clinical trial of genetically engineered pig OHTx as a bridge to allotransplantation.