Inhibition appears to be a common trait of dynamical networks in nature, ranging from neural networks and biochemical networks, to social and technological networks. We here study the role of inhibition in a representative dynamical network model, characterizing the dynamics of random threshold networks (RTNs) with both excitatory and inhibitory links. We find the balance between excitatory and inhibitory links to be a key parameter in the dynamics. Varying the fraction of inhibitory links has a strong effect on the network’s stable population activity A∞ and sensitivity to perturbation λ. We develop mean-field approximations for A∞ and λ, and find that the dynamics is independent of degree distribution in the high degree limit. Instead, the amount of inhibition is a determinant of dynamics and sensitivity, allowing for criticality (λ = 1) only in a specific corridor of inhibition. In a minimal model of an adaptive threshold network we demonstrate how the dynamics remains robust against changes in the topology. This adaptive model can be extended in order to generate networks with a controllable activity distribution and specific topologies.