A model for double-diffusive convection in an anisotropic porous layer with a constant throughflow is explored, with penetrative convection being simulated via an internal heat source. Both linear instability and nonlinear stability analyses are performed to assess the suitability of linear theory to predict the destabilisation of the throughflow. It is shown that due to oscillatory instability modes, there are three distinct regions, where increasing the ascending throughflow from rest actually has a stabilising effect, before following the standard destabilisation and stabilisation pattern. This is a previously unobserved phenomenon. The agreement between the linear and nonlinear thresholds is substantial when a small descending throughflow is introduced, although this does deteriorate for ascending throughflow. (C) 2010 Elsevier Ltd. All rights reserved.