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This thesis contains an asymptotic and numerical study of the effects of travelling modes on the stability of the boundary layer on a rotating smooth broad cone (where a broad cone is defined as a cone with a half angle between ψ = 40◦ and 90◦), and a numerical study of the effects of travelling modes on a rotating broad cone with surface roughness using the Miklavˇciˇc and Wang model. The rotating cone model can be used to theoretically model an aeroengine nose cone. The aim of this thesis is to observe the effects of travelling modes, travelling both faster and slower relative to the rotation speed of the cone, on the stability of the boundary layer of the cone. It was observed that increasing the travelling mode frequency resulted in a slight stabilisation in the type I modes and a strong destabilisation in the type II mode for broad cone half angle, with this effect more amplified the lower the cone half angle. This resulted in the travelling modes with a strong negative frequency, i.e travelling slower than the rotation speed of the cone, producing the most stable case for the smooth broad cone case. We also observed that altering the half angle of a smooth cone resulted in the critical frequency first decreasing between 40◦ and 50◦ then increasing beyond 50◦. Increasing the surface roughness caused a stabilisation in the type I modes for all frequencies, countering the slight destabilisation present in negative frequencies. Increasing concentric and isotropic roughness caused a stabilisation of the type II modes, which counters the destabilisation due to increasing frequency, whereas the streamwise roughness destabilised the type II modes in combination with increasing frequency. Increasing concentric and isotropic roughness caused a critical frequency increase whereas increasing the streamwise roughness reduced the critical frequency.