The finite derivation type property is a homotopical condition on monoids. Craig Squier has proved that a monoid must satisfy it in order to admit a presentation by a finite and convergent rewriting system. We generalise the property to n-categories presented by polygraphs and we recover Squier's theorem when n is 1. However, we prove that this result does not hold anymore for categories of dimension 2 and above. We study several examples of 2-categories presented by finite convergent polygraphs, with or without the property of finite derivation type, in order to illustrate sample cases.