ABSTRACT We have studied the unusual time variability of an ultraluminous X-ray source in M 101, 4XMM J140314.2 + 541806 (henceforth, J1403), using Chandra and XMM-Newton data. Over the last two decades, J1403 has shown short-duration outbursts with an X-ray luminosity ∼1–3 × 1039 erg s−1, and longer intervals at luminosities ∼0.5–1 × 1038 erg s−1. The bimodal behaviour and fast outburst evolution (sometimes only a few days) are more consistent with an accretor/propeller scenario for a neutron star than with the canonical outburst cycles of stellar-mass black holes. If this scenario is correct, the luminosities in the accretor and propeller states suggest a fast spin (P ≈ 5 ms) and a low surface magnetic field (B ∼ 1010 G), despite our identification of J1403 as a high-mass X-ray binary. The most striking property of J1403 is the presence of strong ∼600-s quasi-periodic oscillations (QPOs), mostly around frequencies of ≈1.3–1.8 mHz, found at several epochs during the ultraluminous regime. We illustrate the properties of such QPOs, in particular their frequency and amplitude changes between and within observations, with a variety of techniques (Fast Fourier Transforms, Lomb–Scargle periodograms, weighted wavelet Z-transform analysis). The QPO frequency range <10 mHz is an almost unexplored regime in X-ray binaries and ultraluminous X-ray sources. We compare our findings with the (few) examples of very low frequency variability found in other accreting sources, and discuss possible explanations (Lense–Thirring precession of the inner flow or outflow; radiation pressure limit-cycle instability; marginally stable He burning on the neutron star surface).