Background: The accuracy of electroencephalography (EEG) and magnetoencephalography (MEG) in measuring neural evoked responses (ERs) is challenged by overlapping neural sources. This lack of accuracy is a severe limitation to the application of ERs to clinical diagnostics. New method: We here introduce a theory of stochastic neuronal spike timing probability densities for describing the large-scale spiking activity in neural assemblies, and a spike density component analysis (SCA) method for isolating specific neural sources. The method is tested in three empirical studies with 564 cases of ERs to auditory stimuli from 94 humans, each measured with 60 EEG electrodes and 306 MEG sensors, and a simulation study with 12,300 ERs. Results: The first study showed that neural sources (but not non-encephalic artifacts) in individual averaged MEG/EEG waveforms are modelled accurately with temporal Gaussian probability density functions (median 99.7 %–99.9 % variance explained). The following studies confirmed that SCA can isolate an ER, namely the mismatch negativity (MMN), and that SCA reveals inter-individual variation in MMN amplitude. Finally, SCA reduced errors by suppressing interfering sources in simulated cases. Comparison with existing methods: We found that gamma and sine functions fail to adequately describe individual MEG/EEG waveforms. Also, we observed that principal component analysis (PCA) and independent component analysis (ICA) does not consistently suppress interference from overlapping brain activity in neither empirical nor simulated cases. Conclusions: These findings suggest that the overlapping neural sources in single-subject or patient data can be more accurately separated by applying SCA in comparison to PCA and ICA.