Consider the differential equation \(\dot x=f^ 0(x)+\epsilon f^ 1(\omega t,x;\epsilon)\), \(x\in D\subset R^ n\) where \(f^ 0\) and \(f^ 1\) are sufficiently smooth, \(f^ 1\) is \(2\pi\)-periodic in \(\omega\) t and \(\epsilon\) is a small positive parameter. Let the unperturbed system \(\dot x=f^ 0(x)\) have a hyperbolic point. The paper is concerned with the error estimate for the Melnikov integral \(\int^{\infty}_{-\infty}f^{(0)}(x_ 0^{s,u}(\tau)\wedge f^ 1(\tau,x_ 0^{s,u}(\tau);0)d\tau\) introduced by \textit{P. J. Holmes} [SIAM J. Appl. Math. 38, 65-80 (1980; Zbl 0472.70024)] in order to analyse averaged systems of differential equations.