We study the average Age of Information (AoI) and peak AoI (PAoI) of a dual-queue status update system that monitors a common stochastic process. Although the double queue parallel transmission is instrumental in reducing AoI, the out of order of data arrivals also imposes a significant challenge to the performance analysis. We consider two settings: the M-M system where the service time of two servers is exponentially distributed; the M-D system in which the service time of one server is exponentially distributed and that of the other is deterministic. For the two dual-queue systems, closed-form expressions of average AoI and PAoI are derived by resorting to the graphic method and state flow graph analysis method. Our analysis reveals that compared with the single-queue system with an exponentially distributed service time, the average PAoI and the average AoI of the M-M system can be reduced by 33.3% and 37.5%, respectively. For the M-D system, the reduction in average PAoI and the average AoI are 27.7% and 39.7%, respectively. Numerical results show that the two dual-queue systems also outperform the M/M/2 single queue dual-server system with optimized arrival rate in terms of average AoI and PAoI.