  The asynchronous systems f are multi-valued functions, representing the
non-deterministic models of the asynchronous circuits from the digital
electrical engineering. In real time, they map an 'admissible input' function
u:R\rightarrow{0,1}^{m} to a set f(u) of 'possible states' x\inf(u), where
x:R\rightarrow{0,1}^{m}. When f is defined by making use of a 'generator
function' {\Phi}:{0,1}^{n}\times{0,1}^{m}\rightarrow{0,1}^{n}, the system is
called regular. The usual definition of the serial connection of systems as
composition of multi-valued functions does not bring the regular systems into
regular systems, thus the first issue in this study is to modify in an
acceptable manner the definition of the serial connection in a way that matches
regularity. This intention was expressed for the first time, without proving
the regularity of the serial connection of systems, in a previous work. Our
present purpose is to restate with certain corrections and prove that result.
