A general theory is presented for the electrochemical impedance of multistep mechanisms with only soluble diffusing species and electrons. The Faradaic admittance can be written as (i omega)(1/2) times the ratio of two Ith-order determinants, where I is the number of reaction steps whose stoichiometries are linearly independent. I cannot exceed S - M, where S is the number of chemical species, including electrons, and M is one more than the number of elements (or groups of atoms which remain intact during the reaction). The determinants are polynomials in (i omega(1/2) of degree I - 1 (top determinant) and I (bottom determinant). A method of determining the entries of the determinant by inspection is given. The number of critical frequencies (excluding zero and infinite frequency) of the Faradaic admittance is shown to be 2I - 1, and the relationship of these frequencies to the shape of experimental Bode plots in electrochemical impedance spectroscopy is discussed.