This paper examines the path of an economy constrained by bio-physical limits, due to (i) limited natural capital availability and (ii) compliance with the postulate of strong sustainability. The economy tends towards a stationary state characterized by lower and higher endowments of natural capital and human factors respectively than in the initial state. But this evolution is not monotonous in the sense that GDP and consumption have a path in four phases: growth, reversal, decrease and a quasi-stationary phase leading to steady state. On the contrary, the natural capital stock is declining almost monotonically, involving increasing natural capital operating costs. This results in a structural change by which the human factors share devoted to exploitation increases continuously at the expense of that devoted to final production. Taking pollution into account results in a peak of GDP less pronounced and advanced over time compared to the pollution-free situation.