The article defends the thesis that in the context of moral responsibility (MR) as it is understood in modern Strawsonian theories of MR, psychological approach has significant advantages in comparison with competing approaches to personal identity problem: biological approach, substantialism and narrative view. In the Strawsonian theories, two generally accepted necessary conditions of the appropriateness of holding someone responsible are the conditions of moral agency and agency of action. The article shows that for these conditions to be satisfied a person who is to be hold morally responsible now for some past action should stay not only numerically, but also qualitatively identical in respect to his quality of will and moral capacities. That raises the problem of personal identity over time in the context of MR. It is shown that psychological approach helps to clarify the kind of personal identity that is required for the conditions of moral agency and agency of action to be satisfied, it is compatible with all the Strawsonian theories of MR and copes with much of moral collisions that are usually presented as its problematic consequences. It is also shown that the competing approaches to personal identity are either cannot clarify the relevant for MR kind of personal identity, or incompatible with most of the Strawsonian theories of MR and leads to moral collisions. That gives strong reasons to prefer the psychological approach to personal identity in the context of MR.