Realistic lava flow models require a comprehensive understanding of the rheological properties of lava under a range of stress conditions. Previous measurements have shown that at typical eruption temperatures lavas are non-Newtonian. This is commonly attributed to the formation and destruction of crystal networks. In the present study, the effects of bubbles on the time-dependent, non-Newtonian properties of vesicular melts are investigated experimentally using analogue materials. The shear-thinning behaviour of bubbly liquids is shown to be dependent on the previous shearing history. This thixotropic behaviour, which was investigated using a rotational vane-viscometer, is caused by delayed bubble deformation and recovery when subjected to changes in shear stress. The viscoelastic transition and the transient flow behaviour of analogue fluids were studied using both a rotational vane-viscometer and oscillatory shear apparatus. These experiments have shown that vesicular suspensions are viscoelastic fluids with a yield strength, power law rheology, and a non-zero shear modulus. These properties are also found in polymer fluids commonly used as analogue materials for lava such as gum rosin. We show that, when materials with this rheology are accelerated in channels, they may be fragmented, and when they flow through a narrowing conduit, pulsating flow can develop as a consequence of a transition from slip to non-slip conditions at the conduit wall. This has important implications both for effusive and explosive volcanic eruptions.