in this paper, the possible substitution of conventional with non conventional oil is studied using system dynamics models. The model proposed in this paper is based on geological, economic and technological aspects, and it fits approximately the behaviour observed by Hubbert. A first validation of the model has been made with the USA oil production data. These USA data show that there is a good coincidence between our model and the reality. This model has been expanded in order to include the substitution of the conventional oil with the non conventional one for the World. Two models with different ways to treat the contribution of non conventional oil have been developed and tested: a base model (business as usual), which extrapolates the last two decades' growth of this type of oil into the future, and a model that explores how much non conventional oil would be needed in order to avoid a peak and decrease in the global non renewable fuel production. The results show that, even under some hypotheses that we consider optimistic, the attenuation of the peak oil decline requires more than 10% of sustained growth of non conventional oil production over at least the next two decades. (C) 2009 Elsevier Ltd. All rights reserved.