It has been proven that there are synchrony (or phase-locking) phenomena present in multiple oscillating systems such as electrical circuits, lasers, chemical reactions, and human neurons. If the measurements of these systems cannot detect the individual oscillators but rather a superposition of them, as in brain electrophysiological signals (electro- and magneoencephalogram), spurious phase locking will be detected. Current source-extraction techniques attempt to undo this superposition by assuming properties on the data, which are not valid when underlying sources are phase-locked. Statistical independence of the sources is one such invalid assumption, as phase-locked sources are dependent. In this paper, we introduce methods for source separation and clustering which make adequate assumptions for data where synchrony is present, and show with simulated data that they perform well even in cases where independent component analysis and other well-known source-separation methods fail. The results in this paper provide a proof of concept that synchrony-based techniques are useful for low-noise applications.