Graph pyramids are often used for representing irregular image pyramids. For the 2D case, combinatorial pyramids have been recently defined in order to explicitly represent more topological information than graph pyramids. The main contribution of this work is the definition of pyramids of n-dimensional (nD) generalized maps. This extends the previous works to any dimension, and generalizes them in order to represent any type of pyramid constructed by using any removal and/or contraction operations. We give basic algorithms that allow to build an nD generalized pyramid that describes a multi-level segmented image. A pyramid of nD generalized maps can be implemented in several ways. We propose three possible representations and give conversion algorithms.