Turbidity currents and pyroclastic density currents may originate as stratified flows or develop stratification during propagation. Analogue, density-stratified laboratory currents are described, using layers of salt solutions with different concentrations and depths to create the initial vertical stratification. The evolving structure of the flow depends on the distribution of the driving buoyancy between the layers, B* (proportional to the layer volumes and densities), and their density ratio, ρ*. When the lower layer contains more salt than the upper layer, and so has a greater proportion of the driving buoyancy (B* < 0·5), this layer can run ahead leading to streamwise or longitudinal stratification (ρ*→0), or the layers can mix to produce a homogeneous current (ρ*→1). If the upper layer contains more salt and thus buoyancy (B* > 0·5), this layer travels to the nose of the current by mixing into the back of the head along the body/wake density interface to produce a homogeneous flow (ρ*→1) or overtaking, leading to streamwise stratification (ρ*→0). Timescales describing the mixing between the layers and the streamwise separation of the layers are used to understand these flow behaviours and are in accordance with the experimental observations. Distance–time measurements of the flow front show that strongly stratified flows initially travel faster than weakly stratified flows but, during their later stages, they travel more slowly. In natural flows that are stratified in concentration and grain size, internal features, such as stepwise grading, gradual upward fining and reverse grading, could be produced depending on B* and ρ*. Stratification may also be expected to affect interactions with topography and overall fan architecture.