AbstractThe minimal realization problem of two‐dimensional transfer functions remains unsolved despite numerous efforts to solve it. Most conventional approaches have taken the form of seeking real number solutions for nonlinear equations that have system coefficients as their unknown variables and are therefore not amenable to realization. This paper presents sufficient conditions by which the possibility of minimal realization can be judged without necessarily solving nonlinear equations from the coefficients of optimally given two‐dimensional transfer functions. The sufficient conditions presented here are broad ones that include the well‐known types of separable‐denominator and separable‐numerator. We also introduce the canonical forms of state space representation for the separable denominator type and separable‐numerator type, which are very useful in practical applications, and additionally show that there are cases where realization dimensions can be reduced even for the general transfer function, which is difficult in finding the minimal