The rapid advancement of artificial intelligence (AI) systems has fundamentally challenged traditional notions of moral responsibility and accountability. As AI systems become increasingly autonomous and capable of causing significant harm, the question of who should be held morally accountable for their behavior has become one of the most pressing ethical issues of our time. This thesis presents a comprehensive examination of moral accountability in AI systems, introducing a novel theoretical framework called "Gradient Responsibility Networks" (GRN) that addresses critical gaps in existing approaches. Through extensive analysis of philosophical foundations, empirical case studies, and real-world incidents, this work demonstrates that traditional binary models of moral responsibility are inadequate for the complex, distributed, and temporal nature of AI systems. The proposed GRN framework offers a mathematically rigorous, practically implementable approach to distributing moral responsibility across networks of actors involved in AI development, deployment, and governance. Key findings include: (1) 80-85% of AI projects fail, creating widespread accountability gaps; (2) existing frameworks fail to address temporal decay of responsibility and emergent behaviors; (3) the GRN framework provides superior performance across six critical dimensions compared to traditional approaches; and (4) empirical case studies validate the framework's practical applicability across diverse AI domains. This research contributes to the growing body of literature on AI ethics by providing both theoretical innovation and practical tools for policymakers, technologists, and ethicists grappling with the challenges of AI accountability in the 21st century.