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After many years of research on non-profit organisations (NPOs), the success rate of the projects they manage remains low. This is particularly due to the fact that the awareness of the need for project management competences to achieve project success is poor. This paper aims to close this awareness gap. The purpose of this paper is to examine the relationships between leader-leader exchange (LLX), sharing values, result orientation and personal communication as critical project management competences and their impact on project success in NPOs. The research which is based on social exchange and leadership theories, includes a testing of the research model and hypotheses using the structural equation modelling and bootstrap method. Data were collected during a survey organized in March-May 2023 that targeted more than 100 NPOs in order to apply the quantitative research method. The research findings indicate that the mediating variable “Result-Orientation” has a stronger impact on project success than the positive effect “leadership” and “sharing values” have on project success. However, the significance of leadership and sharing values for project success is increased by personal communication as an important moderating variable. The contribution to the science of this paper lies in the fact that the quantitative method was applied for the first time for the impact study with the chosen project management competences on project success. The practical relevance of the research is to encourage the adoption of social exchange and leadership theories in NPOs, to increase project contribution to civil society.