Summary: For the stability analysis of time-delay systems, the Razumikhin approach provides (at the cost of some conservatism) a set of conditions that are relatively easy to verify when compared to the Krasovskii approach. Unfortunately, for linear Delay Difference Inclusions (DDIs) a verification of these conditions is only possible by solving a Bilinear Matrix Inequality (BMI). To obtain a tractable stability analysis method for DDIs, an alternative set of Razumikhin-type conditions is proposed in this paper, which are based on a technique that was developed for interconnected systems in Willems (1972). In particular, via the proper selection of storage and supply functions, these conditions can be used to establish Input-to-State Stability (ISS) for general DDIs. When linear DDIs and quadratic functions are considered, \(\ell _{2}\)-disturbance attenuation can be established by solving a single Linear Matrix Inequality (LMI). Moreover, this LMI is shown to be less conservative than the BMI corresponding to the existing Razumikhin-type conditions for linear DDIs.