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Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow is investigated numerically by an immersed boundary-lattice Boltzmann method. The leading edge of the leading foil is forced to undergo both heave and pitch motions, while the leading edge of the trailing foil is forced to undergo heave motion only. Of particular interests are the effects of stream-wise gap distance Gx (Gx/c = 0.25–1.75, where c denotes the length of the foil) and the phase difference Φ between the heave motions of the foils (Φ/π = −1.00 to 1.00) on the hydrodynamic characteristics of the foils, such as the propulsive force, the propulsive efficiency, the passive deformation, and the flow field around the foils. For the leading foil, because of the existence of the trailing foil and the resulting gap flow between the foils, the propulsive performance is noticeably influenced by Φ at small Gx/c values and such an influence is weakened with increasing Gx/c. For the trailing foil, the propulsive performance is primarily affected by Φ, and the physics behind such a strong effect is that Φ dictates the manner by which the vortices shed from the leading foil interact with the trailing foil. In contrast, the interaction of the vortices shed from the leading foil with the trailing foil is not significantly affected by Gx/c because the trailing foil experiences similar vortices shed from the leading foil, regardless of Gx/c. With different Gx/c and Φ/π values, three distinct deformation states of the foils, namely, the symmetric periodic state, the asymmetric periodic state, and the irregular state, are identified and are mapped out in the (Φ/π, Gx/c) space. Good correlation between the deformation state of the foils and the propulsive performance of the trailing foil has been observed.