Simple shear deformation experiments on three-phase, hydrous, haplogranitic magmas, composed of quartz crystals (24–65 vol.%), CO₂-rich gas bubbles (9–12 vol.%) and melt in different proportions, were performed with a Paterson-type rock deformation apparatus. Strain rates from 5 · 10⁻⁶ s⁻¹ to 4 · 10⁻³ s⁻¹ were applied at temperatures between 723 and 1023 K and at pressure of 200 MPa. The results show that the three-phase suspension rheology is strongly strain rate dependent (non-Newtonian behavior). Two non-Newtonian regimes were observed: shear thinning (viscosity decreases with increasing strain rate) and shear thickening (viscosity increases with increasing strain rate). Shear thinning occurs in crystal-rich magmas (55–65 vol.% crystals; 9–10 vol.% bubbles) as a result of crystal size reduction and shear zoning. Shear thickening prevails in dilute suspensions (24 vol.% crystals; 12 vol.% bubbles), where bubble coalescence and outgassing dominate. At intermediate crystallinity (44 vol.% crystals; 12 vol.% bubbles) both shear thickening and thinning occur. Based on the microstructural observations using synchrotron radiation X-ray tomographic microscopy, bubbles can develop two different shapes: oblate at low temperature (<873 K) and prolate at high temperature (>873 K). These differences in shape are caused by different conditions of flow: unsteady flow, where the relaxation time of the bubbles is much longer than the timescale of deformation (oblate shapes); steady flow, where bubbles are in their equilibrium deformation state (prolate shapes). Three-phase magmas are characterized by a rheological behavior that is substantially different with respect to suspensions containing only crystals or only gas bubbles.