A recent study of Cane et al. <2003> showed that in some intense SEP events, the time-intensity profiles exhibit two peaks, with an earlier one having a high Fe/O and a later one with a low Fe/O ratio. They suggested that these two-component events are due to CMEs and their accompanying flares occurring together, with the first peak being flare-related and the second peak being CME-driven shock related. In this paper, we develop a model which examines particle acceleration and transport when both flares and CME-driven shocks are present. We study time-intensity profiles for three different scenarios: a pure shock case, a pure flare case and a shock-flare-mixed case. Using reasonable estimates of the relative timing between CMEs and associated flares, we find that a large portion of the flare accelerated material is subject to absorption and re-acceleration by the CME-driven shock. Consequently, the time intensity profile for the shock-flare-mixed case shows an initial rapid increase, owing to particles accelerated at the flare and followed by a plateau similar to that of a pure shock case.