Time-resolved particle image velocimetry and hot-wire anemometry are employed to examine the spectral characteristics and frequency-dependent convection velocities of a turbulent boundary layer developing over an axisymmetric body of revolution subjected to varying pressure gradients and curvature. After a predominantly zero pressure-gradient (ZPG) cylindrical mid-body, the boundary layer contracts under a favourable pressure gradient (FPG), recovers under a mild adverse pressure gradient (APG) and thickens rapidly along the curved tail under a strong APG. Outer-scaled premultiplied spectra collapse well at high frequencies, whereas the low frequencies collapse only partially across the mid-body and into the tail, while the peak energy associated with the intermediate frequencies decreases downstream before rising again under the strong APG. Rescaling spectra using the equivalent flat-plate ZPG boundary-layer thickness improves collapse, highlighting the influence of upstream history and the persistence of ZPG-like turbulence organisation. Across most of the body, the spectral characteristics remain dominated by the upstream ZPG development despite the onset of pressure gradients and curvature. This interpretation is further supported by frequency-dependent coherence, two-point correlations and inclination-angle analysis, which show turbulence organisation largely consistent with the ZPG case along the body. The frequency-dependent convection velocities, upper U Subscript c <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> mml:msub mml:miU</mml:mi> mml:mrow mml:mrow mml:mic</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> UcU_{{c}} , display stronger sensitivity to local flow conditions. Near the wall, low frequencies convect faster than the local mean, while intermediate frequencies, corresponding to the peak energy content, follow a progression from faster-than-mean near the wall, to matching the mean and then slower-than-mean farther out. For both low- and intermediate-frequency bands, the wall-normal extent of faster-than-mean upper U Subscript c <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> mml:msub mml:miU</mml:mi> mml:mrow mml:mrow mml:mic</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> UcU_{{c}} regions expands under FPG and contracts under APG, while slower-than-mean upper U Subscript c <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> mml:msub mml:miU</mml:mi> mml:mrow mml:mrow mml:mic</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:math> UcU_{{c}} regions show the opposite trend. This is consistent with two-point correlations in the body-axis frame, which show that structure orientation is largely maintained as the flow evolves with increasing curvature and APG.