A turbulent boundary layer subjected to multiple, additional strain rates, namely convex curvature coupled with zero, favorable, and adverse streamwise pressure gradients (ZPG, FPG, and APG) was investigated experimentally. The Reynolds stresses were suppressed, with respect to flat plate values, due primarily to the effects of strong convex curvature (&dgr;0/R≊0.10). Combined with curvature, the FPG reduced the strength of the wake component, resulted in a greater suppression of the fluctuating velocity components, and a reduction of the primary Reynolds shear stress relative to the ZPG curved case, whereas the APG counteracted the stabilizing curvature effect. The additional influence of streamwise pressure gradients on the normal stresses is most apparent in the outer part of the boundary layer (y+≥100). However, the primary Reynolds shear stress is impacted by the additional strain rates throughout most of the boundary layer, especially for the strong pressure gradients. Using theuv2quadrant burst detection method, including grouping of ejections, the normalized mean burst period in the convex boundary layer was found to increase in the presence of FPG and to decrease for APG. The time between bursts increased locally (by as much as 75%) in regions of locally strong acceleration. As the pressure gradient was relaxed to zero downstream, the bursting frequency in the case with stronger initial acceleration remained suppressed compared to that with milder initial acceleration, indicating a strain‐rate history dependence. ©1996 American Institute of Physics.