A necessary and sufficient condition for a linear sequential circuit to possess a feedforward inverse is given for the class of linear sequential circuits that possess delay-free inverses. Unlike previous work, this condition is given in terms of the difference (state) equation matrices rather than minors of the system transfer-function matrix. The constructive proof yields the following corollary: if a linear sequential circuit requiringnmemory elements has a feedforward delay-free inverse, then there exists at least one such inverse that requires no more thannmemory elements.