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The performance augmentation mechanism of a tandem-foil system undergoing time-asymmetric flapping with unequal up- and downstroke durations (velocities) is investigated at three different phase angles, 0°, 90°, and 180°. Specifically, an asymmetry ratio, ranging from 0 to 0.4, is introduced to quantify the degree of the stroke time-asymmetry and to serve as the primary kinematic parameter of interest that affects the foil performances. Numerical simulations are implemented to predict the force production and to investigate the associated mechanism at different asymmetry ratios and phase angles. Validations are performed using digital particle image velocimetry in water tunnel experiments with two identical 3D printed wings. The results suggest that the foil performances at proper phase angles can be enhanced by stroke time-asymmetry. The force production during in-phase flapping obtains 15% increment while that during counterstroke flapping achieves remarkable enhancements by 2.5 times, as the asymmetry ratio increases from 0 to 0.4. The study also demonstrates that such enhancements are achieved through the changes in foil flapping velocities and foil-vortex interactions between the unequal up- and downstrokes. These findings not only provide insights toward the characteristics of tandem foils which are operated in non-sinusoidal flapping strokes but also offer a reference to the design of efficient wing kinematics for high-performance biomimetic propulsors. [ABSTRACT FROM AUTHOR]