Promoting coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration is not only a major national strategy,but also a long-term complex process.It is necessary to apply scientific theories and respect the laws of nature to realize the strategic target of common prosperity,share a clean environment,share the burden of risk of development,and build a world-class metropolis for the Beijing-Tianjin-Hebei Urban Agglomeration.This article examines the scientific foundation and patterns of coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration.Synergy theory,game theory,dissipative structure theory,and catastrophe theory are the theoretical basis of coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration.Synergy theory is the core theory for the coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration.The coordinated development process of the Beijing-Tianjin-Hebei Urban Agglomeration is a non-linear spiral progress of game,coordination,mutation,game,resynchronization,and mutation.Each game-coordination-mutation process promotes the coordinated development of the urban agglomeration to a higher level of coordination,and the progress fluctuates.This process includes eight stages:assistance phase,cooperation phase,harmonization phase,synergy phase,coordination phase,resonance phase,integration phase,and cohesion phase.Further analysis shows that the real connotation of coordinated development of the BeijingTianjin-Hebei Urban Agglomeration is to realize the coordination of planning,transportation,industrial development,urban and rural development,market,science and technology,finance,information,ecology,and the environment,as well as the construction of a collaborative development community.The Beijing-TianjinHebei Urban Agglomeration will achieve advanced collaboration from low-level collaborative phase through regional coordination on planning,construction of traffic network,industrial development,joint development of urban and rural areas,market consolidation,science and technology cooperation,equal development of financial services,information sharing,ecological restoration,and pollution control.This study may provide a scientific foundation and theoretical basis for the coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration.