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Reachability and observability Gramians are defined for the descriptor systems and . The pencils and are assumed to be regular. If is singular,these Gramians do not, in general, satisfy the "expected" Lyapunov-like (Sylvester) equations (for example, if is the continuous-time teachability Gramian). This is shown by expressing the solution of the descriptor system in terms of the parameters of the Laurent expansion of or . We derive the Lyapunov-like equations which these Gramians do satisfy.