A complete algebraic theory of invertibility of linear systems Σ described by differential-difference equations with commensurable delays is developed, introducing the notion of k-integral, l-delay inverse. Considering the transfer-function matrix, the matrix fraction, and Rosenbrock's system matrix descriptions respectively in the forms q -1(s, σ)T(s, σ) , Q -1(s, σ)P(s, σ) , and V(s, σ) = sI −F G −H J , where q( s, σ) is a polynomial; T( s, σ), Q( s, σ), and P( s, σ) are p × r, p × p, and p × r matrices over R [ s, σ]; and F, G, H, and J are n × n, n × r, p × n and p × r matrices over R [ σ] of the system Σ, NASCs for invertibility of the delay systems in the above sense are shown to depend on a new notion of weak monicity of a polynomial g( s, σ) over R [ s, σ] constructed from the minors of T( s, σ), P( s, σ), or the system matrix V( s, σ), while for a stable inverse with or without delay, in addition to the property of stable weak monicity, a rank condition at complex points of a row vector constructed from the same matrices is also to be satisfied. This paper demonstrates that apart from the full-rank property of the matrix T( s, σ), P( s, σ), or V( s, σ) which constitutes the NASC for inversion of delay-free systems, the concept of weakly monic (stable) polynomials plays the major role in deciding the invertibility of delay systems. These criteria of invertibility are then employed to establish NASCs for regulability of systems with commensurable delays under feedback. The paper is concluded with a detailed description of a constructive procedure establishing the pertinent existence theorems as to how the inherent integrations and the inherent delays of Σ are determined and a stable inverse with minimum delays and minimum integrations is computed. The novelty of this construction procedure is that the inverse system is generated via the theory of realization.