This paper begins with a complete description of the complex Poynting theorem

followed by a rigorous study of the generalized resonance in a multi-antenna system.We discuss the condition generating the generalized resonance

which is the balance of the electromagnetic field energies stored in the antenna open system.The matrix expression of the generalized resonant factor is derived.Based on the energy dependence

we introduce the generalized Foster theorem for an arbitrary antenna system and the network quality factor

Q

to further describe the behaviors of the generalized resonance.Some practical examples show that the generalized resonance may take on the phenomena of strong and sharp field in the near field region and super-directivity in the far field region of the antenna system.