Key points Large premotor neurons of the cerebellar nuclei (CbN cells) integrate synaptic inhibition from Purkinje neurons and synaptic excitation from mossy fibres to generate cerebellar output. We find that mossy fibre inputs to CbN cells generate unitary AMPA receptor EPSCs of ∼1 nS that decay in ∼1 ms and mildly voltage‐dependent NMDA receptor EPSCs of ∼0.6 nS that decay in ∼7 ms. A few hundred mossy fibres active at a few tens of spikes s−1 must converge on CbN cells to generate physiological CbN spike rates (∼60 spikes s−1) during convergent inhibition from spontaneously active Purkinje cells. Dynamic clamp studies in cerebellar slices from weanling mice demonstrate that synaptic excitation from mossy fibres becomes more effective at increasing the rate of CbN cell spiking when the coherence (synchrony) of convergent inhibition is increased. Abstract Large projection neurons of the cerebellar nuclei (CbN cells), whose activity generates movement, are inhibited by Purkinje cells and excited by mossy fibres. The high convergence, firing rates and strength of Purkinje inputs predict powerful suppression of CbN cell spiking, raising the question of what activity patterns favour excitation over inhibition. Recording from CbN cells at near‐physiological temperatures in cerebellar slices from weanling mice, we measured the amplitude, kinetics, voltage dependence and short‐term plasticity of mossy fibre‐mediated EPSCs. Unitary EPSCs were small and brief (AMPA receptor, ∼1 nS, ∼1 ms; NMDA receptor, ∼0.6 nS, ∼7 ms) and depressed moderately. Using these experimentally measured parameters, we applied combinations of excitation and inhibition to CbN cells with dynamic clamp. Because Purkinje cells can fire coincident simple spikes during cerebellar behaviours, we varied the proportion (0–20 of 40) and precision (0–4 ms jitter) of synchrony of inhibitory inputs, along with the rates (0–100 spikes s−1) and number (0–800) of excitatory inputs. Even with inhibition constant, when inhibitory synchrony was higher, excitation increased CbN cell firing rates more effectively. Partial inhibitory synchrony also dictated CbN cell spike timing, even with physiological rates of excitation. These effects were present with ≥10 inhibitory inputs active within 2–4 ms of each other. Conversely, spiking was most effectively suppressed when inhibition was maximally asynchronous. Thus, the rate and relative timing of Purkinje‐mediated inhibition set the rate and timing of cerebellar output. The results suggest that increased coherence of Purkinje cell activity can facilitate mossy fibre‐driven spiking by CbN cells, in turn driving movements.