With the development of robotics science, lots of research has been conducted in the area of biped robots and many industries have been attracted to the application of these robots. Because of the non-continuous nature of legged robots and bipeds in particular, not facing problems that wheeled or snake-like robots do in moving on stairs and ditches, their industrial and practical applications has been considered seriously. That is why a great number of humanoid robots have been developed all over the world and in some countries such as Japan, development of Humanoid Robots is considered as a national project to the extent that it is considered as an index of the science and technology development in the country. As the humanoid robots have the same structure as humans, many efforts are put to reach their level of ability to handle many tasks which have been normally assigned to humankind. Among the subjects which have been studied on biped motion, naming motion stability analysis, motion pattern generation, optimization, and control, the stability and control of these systems can be considered as one of the most important issues. The concept of stability of the biped motions, its criteria and how such stability can be guaranteed is of the greatest importance for researchers and at the same time is the most complicated dilemma not completely resolved yet. Most of the researches on stability and control of these systems have been based on the Postural Stability which regards the control of walkers’ stability as the motion tracking of their joints and support limbs on some desired trajectories having postural stability. However, recently some scholars developed the concept of the stability of walkers correctly and equate it with not going to the states which leads to fall down or tip over. The current research is based on this new intuition of stability and unlike the traditional analyses which follows stability and control of the walker in joint space as internal or detailed quantities, a walker is considered as a total system so that the problem is followed in whole-body momentum space . Such an approach gives an exhaustive solution which enables its implementation on any biped walkers considering the existence of a map between these two spaces. Firstly, Principle Equation of Motion (for walkers) is derived that later results in introducing two piecewise-continuous dynamical systems namely Simplified Walking Model (SWM) and Complete Walking Model (CWM) which both describe the behavior of walker with emphasis on the motion in horizontal plane. Furthermore, by making some realistic assumptions based on human natural walking, a simplified equation of motion named Step-to-Step Equation of Walking is formulated. To calculate the solution of steady walking motions, the repetition condition is exerted on this equation that yields a significant finding named Simple and Compound Motion Cycles as general solutions of steady walking. Among all possible motion cycles, Simple Forward Motion Cycle is representing the normal walking pattern. These cycles have marginal stability that in practice cause the motion to diverge exponentially even under slight disturbance. By defining the stabilization of walking as the guidance of the motion initiated from arbitrary initial states to a desired motion cycle and controlling the motion about it, two major strategies are presented for stability control of the walkers: 1) Continuous altering of Center of Pressure (CoP) within support polygon, and 2) Continual planning of the step length and duration. Using these two strategies and based on Simplified Walking Model (SWM), four methods of stability control named generally as Motion Cycle Stabilizers are proposed and their theoretical aspects are iected. Then, to examine the capability and detect deficiencies of the proposed stabilizers on Complete Model of Walking (CWM), some simulations are performed on a physical model with realistic constraints. Finally, to overcome the deficiencies of the Stabilizers, method of Optimal Stability Control is proposed to complete the solution. The numerical simulations show that the proposed approach to the stability and control of biped walkers provides us with a more complete and accurate solution compared with traditional approaches and guarantee the stability of walkers in a maximum sense. Keywords Stability of Walkers, Walking Biped Robots, Walking Model in Momentum Space, Walking Motion Cycles, Stabilization of Walking, Step-to-Step Control of Walking.