The Increment Ratio (IR) statistic (see (1.1) below) was introduced in Surgailis et al. [16]. The IR statistic can be used for testing nonparametric hypotheses for d-integrated (−1/2 < d < 5/4) behavior of time series, including short memory (d = 0), (stationary) long-memory (0 < d < 1/2), and unit roots (d = 1). For stationary/stationary increment Gaussian observations, in [16], a rate of decay of the bias of the IR statistic and a central limit theorem are obtained. In this paper, we study the asymptotic distribution of the IR statistic under the model Xt = Xt0 + gN(t) (t = 1, …, N), where Xt0 is a stationary/stationary increment Gaussian process as in [16], and gN(t) is a slowly varying deterministic trend. In particular, we obtain sufficient conditions on Xt0 and gN(t) under which the IR test has the same asymptotic confidence intervals as in the absence of the trend. We also discuss the asymptotic distribution of the IR statistic under change-points in mean and scale parameters.