Simultaneous orthokinetic and perikinetic coagulations (SOPCs) are studied for small and large Peclet numbers (Pe) using Brownian dynamics simulation. The results demonstrate that the contributions of the Brownian motion and the shear flow to the overall coagulation rate are basically not additive. At the early stages of coagulation with small Peclet numbers, the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to Pe1/2, while with high Peclet numbers, the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to Pe−1/2. Moreover, our results show that the aggregation rate generally changes with time for the SOPC, which is different from that for pure perikinetic and pure orthokinetic coagulations. By comparing the SOPC with pure perikinetic and pure orthokinetic coagulations, we show that the redistribution of particles due to Brownian motion can play a very important role in the SOPC. In addition, the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different. This perspective explains the behavior of coagulation due to the joint effects of the Brownian motion (perikinetic) and the fluid motion (orthokinetic).