In order to describe the evolution of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space in the course of time, and we find the value of the volume asymptotically. Then, using the concept of the volume of the attainable structures, we provide a method to evaluate the ‘age' of the system in continuous and discrete time. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures.