<p>Partitioned algorithm with variable time step is designed for a coupled fluid-fluid interaction problem, which includes two Navier–Stokes equations coupled by some nonlinear interface conditions. The algorithm combines a first-order backward Euler scheme with variable time step for temporal discretization and explicit second-order extrapolation for convection and interface terms. Theoretically, we demonstrate the unconditional stability of the proposed algorithm and establish its convergence analysis. Additionally, based on the previous algorithm, we construct two adaptive time step algorithms. Numerically, some numerical experiments are provided to test the theoretical results, which illustrate the accuracy and efficiency of the presented partitioned algorithm.</p>