This paper discussed the controllability and observability of the regular continuous generalized systems and regular discrete generalized systems, proved that if these systems meet certain conditions, their controllability and observability are equiva- lent. Generalized the conditions to the normal continuous systems and the normal discrete systems,in this paper,we presented a suf- ficient condition for the continuous singular system＇s slow subsystem and the normal system when they were both controllable and observable. The article also explained that some results need to be further sudied in the continous time - varying systems.%文章讨论了线性正则广义系统、正则广义离散系统的能控性和能观性，证明了这些系统在满足某些条件时，它们的能控性和能观性是等价的。同时还把这些条件推广到了正常连续系统和正常离散系统和时变系统，给出了广义系统的慢子系统或正常系统同时能控且能观的一个充分条件，并解释了有两种条件对时变连续系统来说还需要得到进一步的研究。
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