The first-passage failure of a single-degree-of-freedom hysteretic system with nonlocal memory is investigated. The hysteretic behavior is described through a Preisach model with excitation selected as Gaussian white noise. First, the equivalent nonlinear non-hysteretic system with amplitude-dependent damping and stiffness coefficients is derived through generalized harmonic balance technique. Then, equivalent damping and stiffness coefficients are expressed as functions of system energy by using the relation of amplitude to system energy. The stochastic averaging of energy envelope is adopted to accept the averaged It stochastic differential equation with respect to system energy. The establishing and solving of the associated backward Kolmogorov equation yields the reliability function and probability density of first-passage time. The effects of system parameters on first-passage failure are investigated concisely and validated through Monte Carlo simulation. The first-passage failure of a single-degree-of-freedom hysteretic system with nonlocal memory is investigated. The hysteretic behavior is described through a Preisach model with excitation selected as Gaussian white noise. First, the equivalent nonlinear non-hysteretic system with amplitude Then, the equivalent damping and stiffness coefficients are expressed as functions of system energy by using the relation of amplitude to system energy. The stochastic averaging of energy envelope is adopted to accept the averaged The established and solving of the associated backward Kolmogorov equation yields the reliability function and probability density of first-passage time. The effects of system parameters on first-passage failure are investigated concisely and validated through Monte Carlo simulation.