Context : Aims : Using high-quality , broad-band afterglow data for GRB 091029 , we test the validity of the forward-shock model for gamma-ray burst afterglows . Methods : We used multi-wavelength ( NIR to X-ray ) follow-up observations obtained with the GROND , BOOTES-3/YA and Stardome optical ground-based telescopes , and the UVOT and the XRT onboard the Swift satellite . The resulting data of excellent accuracy allow us to construct a multi-wavelength light curve with relative photometric errors as low as 1 % , as well as the well-sampled spectral energy distribution covering 5 decades in energy . Results : The optical/NIR and the X-ray light curves of the afterglow of GRB 091029 are almost totally decoupled . The X-ray light curve shows a shallow rise with a peak at \sim 7 ks and a decay slope of \alpha \sim 1.2 afterwards , while the optical/NIR light curve shows a much steeper early rise with a peak around 400 s , followed by a shallow decay with temporal index of \alpha \sim 0.6 , a bump and a steepening of the decay afterwards . The optical/NIR spectral index decreases gradually by over 0.3 before this bump , and then slowly increases again , while the X-ray spectral index remains constant throughout the observations . Conclusions : To explain the decoupled light curves in the X-ray and optical/NIR domains , a two-component outflow is proposed . Several models are tested , including continuous energy injection , components with different electron energy indices and components in two different stages of spectral evolution . Only the last model can explain both the decoupled light curves with asynchronous peaks and the peculiar SED evolution . However , this model has so many unknown free parameters that we are unable to reliably confirm or disprove its validity , making the afterglow of GRB 091029 difficult to explain in the framework of the simplest fireball model . This conclusion provides evidence that a scenario beyond the simplistic assumptions is needed to be able to model the growing number of well-sampled afterglow light curves .