Dynamic spectrum management is recognized as a key technique to tackle interference in multi-user multi-carrier communication systems and networks. However existing dynamic spectrum management algorithms may not be suitable when the available computation time and compute power are limited, i.e., when a very fast responsiveness is required. In this paper, we present a new paradigm, theory and algorithm for real-time dynamic spectrum management (RT-DSM) under tight real-time constraints. Specifically, a RT-DSM algorithm can be stopped at any point in time while guaranteeing a feasible and improved solution. This is enabled by the introduction of a novel difference-of-variables (DoV) transformation and problem reformulation, for which a primal coordinate ascent approach is proposed with exact line search via a logarithmicly scaled grid search. The concrete proposed algorithm is referred to as iterative power difference balancing (IPDB). Simulations for different realistic wireline and wireless interference limited systems demonstrate its good performance, low complexity and wide applicability under different configurations.