Hydrodynamic instability in lean premixed gas turbine combustors can cause coherent flow velocity oscillations. These can in turn drive heat release oscillations that when favourably coupled with combustor acoustic modes can result in combustion instability. The aim of this paper is to understand the impact of fuel staging on the characteristics of hydrodynamic modes in multi-nozzle combustors. We extend our recent numerical study on the hydrodynamic stability characteristics of a multi-nozzle combustor having three nozzles in a straight line with uniform fuel-air ratio in each nozzle, to the non-uniform fuel-air ratio case. As before we construct the base flow model for this study by super-posing contributions from individual nozzles, determined using a base flow model for a nominally axi-symmetric single nozzle, at every point in the computational domain. The impact of fuel staging is captured by changing the burnt to unburnt gas density ratio parameter in the individual contribution from each nozzle. We investigate the characteristics of the most locally absolutely unstable mode for two cases. The first one is when the middle nozzle is made fuel rich when compared to the side nozzles and the second is when the side nozzles are made fuel rich relative to the middle nozzle. The impact of non-uniform fuel/air ratio on the local absolutely unstable temporal eigenvalues is seen to be small. However, significant changes in the spatial structure of the flow oscillations associated with the hydrodynamic eigen-modes are observed. In the first case, the flow oscillations with a different locally azimuthal nature on the middle nozzle when compared to the side nozzles emerge as the middle nozzle is made richer. In the second case, the oscillations on the two side nozzles are suppressed leaving the middle nozzle in a state that closely matches that of a single unconfined nozzle with the same nominal base flow velocity field. These types of inter-nozzle variations in flow oscillation characteristics can explain the emergence of non-uniformity in heat release oscillation characteristics between individual nozzles in multi-nozzle combustors.