A number of advanced concepts of water resources planning are investigated in order to develop practical methodologies for optimization of water resources systems. Two new methodologies are developed: the discrete differential dynamic programming (DDDP), and the multi-level optimization model (MLOP). The DDDP is a computer program which can overcome the multi-dimensional difficulty often involved in the optimization of a complex water resources system; it can greatly save the cost of analysis by reducing the required computer storage capacity to several hundredths of and the required computer time to tenths of those required by the conventional dynamic programming technique. The MLOM is a novel scheme to resolve a complicated water resources system into a form that can be optimized at several levels for a general solution. These methodologies are being introduced to actual water resources planning processes. Principles and procedures of DDP and MLOP are described including an optimal operation of a reservoir network for hydropower and irrigation, and a two-level optimization of farm irrigation systems (TLOM). (Author)