The paper explores some of the issues involved in constructing measures of mobility when the data are provided in the form of a transition matrix. An initial set of axioms is proposed which is inconsistent. They can, however, be reconciled if empirically unlikely transition matrices are eliminated from consideration. The paper then discusses the problem of comparing matrices not defined over the same interval. An index based on the convergence speed in a Markvov chain process is able to compensate for differing time periods.