<p>This study proposes a mixture of linear and nonlinear Hawkes processes to analyse seismic activity. The linear Hawkes process is the epidemic-type aftershock sequence (ETAS) model. This model is widely accepted in seismology and other scientific fields and is regarded as a current standard stochastic model of earthquake occurrence patterns. The nonlinear Hawkes process is the Dieterich model that originated from the physical characteristics of friction. The mixture model was applied to two aftershock sequences and two swarm-type ones to evaluate its performance. In the fitting to the two swarm sequences, the mixture model is superior to the ETAS and Dieterich models, whereas it is inferior in the fitting to the two aftershock sequences. The swarm sequences will be dominated by the interaction between an external factor and the self-exciting process; the proposed mixture model will be suitable to capture such a complex process.</p>