The simulation of the rainfall-runoff relationship in calibration as well as in control (validation) mode relies on finite-length input and output time series (rainfall, potential evapotranspiration and discharge). Therefore a simulation always consists in a set of behavioral laws together with a set of initial conditions, and we might not be surprised that the misspecification of the latter might yield poor simulations. It is a common practice in hydrology to 'sacrifice' a short part of the available data(typically 1 or 2 years) as a 'warm-up' period in order to initialize the model's state variables before starting to compute the error function. However, we may still encounter catchments for which such a short period is not enough to 'forget' the initial condition. We will try to identify those 'elephant' catchments and the way to deal with them. We will test a couple of solutions that may be used to initialize a model (namely, the GR4J daily time step model) in the case of long-term memory effects. Those solutions range from the full optimization of initial conditions (together with the model's structural parameters) to more robust ones, such as the identification of the asymptotic behavior of the model when some of its parameters reach extreme values.