We characterise novel propagation modes that occur when semi-infinite air fingers and finite air bubbles displace viscous fluid from microchannels. The presence of an axially-uniform rectangular occlusion within a rectangular cross-section leads to a mul- tiplicity of modes, in contrast to the single symmetric mode present in unoccluded channels. For air fingers, the asymmetric 1, oscillatory 2 and localised modes 3 first identified in millimetric channels persist at the micron-scale, confirming that significant gravitational effects are not necessary to support these states. Sufficiently large finite bubbles exhibit analogous modes with quanti- tatively similar flow measures, indicating that the physical mechanisms supporting the propagation modes of finite bubbles are the same as those identified for the air fingers 4. In contrast to the air fingers, in which oscillations are always initiated near the finger tip and propagate backwards, oscillations in finite bubbles can arise from either end of the bubble.