State-of-the-art simulations of detailed neurons follow the Bulk Synchronous Parallel execution model. Execution is divided in equidistant communication intervals, with parallel neurons interpolation and collective communication guiding synchronization. Such simulations, driven by stiff dynamics or wide range of time scales, struggle with fixed step interpolation methods, yielding excessive computation on intervals of quasi-constant activity and inaccurate interpolation of periods of high volatility in solution. Alternative adaptive timestepping methods are inefficient in parallel executions due to computational imbalance at the synchronization barriers. We introduce a distributed fully-asynchronous execution model that removes global synchronization, allowing for long variable timestep interpolations of neurons. Asynchronicity is provided by point-to-point communication notifying neurons’ time advancement to synaptic connectivities. Timestepping is driven by scheduled neuron advancements based on interneuron synaptic delays, yielding an exhaustive yet not speculative execution. Benchmarks on 64 Cray XE6 compute nodes demonstrate reduced number of interpolation steps, higher numerical accuracy and lower runtime compared to state-of-the-art methods. Efficiency is shown to be activity-dependent, with scaling of the algorithm demonstrated on a simulation of a laboratory experiment.