Besides optical fibers are excellent communication media, they are attractive for real time, high speed signal processing on the ground of that they possess very nice merits such as low-loss, large bandwidth-delay product, light weight, and immunity to electromagnetical interferences. A typical optical fiber signal processing device is composed of light sources, delay lines, attenuators, directional couplers, and photodetectors. Many various functions such as frequency filtering, convolution, pulse compression, high speed pulse generation, encoding, and decoding for the incoherent optical fiber signal processing devices are reported in the literature. Recently the lattice optical fiber structures are investigated intensively due to convenience for mathematical formulation and implementation. Although the optical fiber signal processing devices have many attractive features, they have inherent constraints owing to positive system properties, i.e. nonnegative quantities of signals(optical intensities), attenuations, and coupling coefficients. The constraints of the finite impulse response (FIR) optical fiber filters were presented. In this paper, we establish the constraints of the infinite impulse response (IIR) optical fiber filters by means of investigating the possibility of designing the filters with the desirable properties such as maximally flat or equiripple responses. In addition, the characteristics and design principles of the optical fiber filters can be clearly understood from the processes. The mathematical derivation makes use of the state-variable analysis technique to approach this problem. This technology is suitable to describe for both cases: FIR and IIR. Hence the confirmed constraints can be directly applied to the FIR case.