The response matrix equations (RME) are analyzed from two points of view: (a) their computational feasibility, and (b) their consistency with other methods used in reactor analysis. It is shown that RME can be derived directly from the weak form of the diffusion equation without the concept of partial currents, and hence, are also applicable to the description of phenomena, where partial currents have no physical meaning (for example, the conduction of heat). By splitting the high-order RME into a coupled system of single-order equations, the analysis of the convergence properties of the iterative solutions to RME could be greatly simplified. The derived explicit expressions for the convergence ratio were verified by numerical experimentation. As an illustration, the well-known International Atomic Energy Agency benchmark problem has been calculated by two two-dimensional response matrix programs at ASEA-ATOM, CIKADA, and LABAN. In the second part of the paper, the relation of RME to finite difference (FD) equations has been investigated. It was shown that for small mesh sizes, RME are computationally not feasible. For rectangular nodes, an algorithm called the “vectorial model” (VM) was developed, which reduces the amount of unknowns in RME by a factor of 2. This is a generalization to two- and three-dimensional nodes of the author's earlier results. An approximate reduction of VM to scalar equations (one unknown per node) has been discussed, and its relation to recent developments in nodal methods has been emphasized. Several ideas in this paper, such as the improved FD scheme, are far from being completed and therefore should be challenging for further investigation.