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The instability of wake of an axisymmetric body with the NACA aerofoil section was experimentally studied under low background turbulence. The body was suspended using a magnetic suspension and balance system to avoid undesirable influences of mechanical supports on the disturbance development. The Reynolds number based on the chord length of the aerofoil section ranged from 5.3 × 104 to 2.1 × 105. For the body with a NACA0015 aerofoil section where there is no boundary-layer separation on the body surface, the wake was convectively unstable, even at the highest Reynolds number examined. Although the wake maintained axisymmetry of mean flow, the instability waves often took a planar-symmetric form, indicating that the occurrence of disturbance can be influenced by minute variations in the position and orientation of the suspended body. For bodies with thicker NACA0018 and NACA0024 aerofoil sections where the flow involved a region of absolute instability immediately downstream of the trailing edge, the global mode could grow rapidly and attain saturation amplitude within a very short distance from the trailing edge despite that the region of absolute instability was limited only to small streamwise distance, about one tenth of the instability wavelength. The predominant frequency of vortex shedding was found to be very close to the absolute frequency near the trailing edge, especially at the upstream boundary of the region of absolute instability. This is consistent with the theoretical model for the development of a nonlinear global mode. It was also found that the mean flow axisymmetry was broken around the critical Reynolds number for global instability, which led to the appearance and growth of a planar-symmetric global mode.