The critical dynamics of the nonperiodic ferromagnetic Ising chains with two different coupling constants (J1＞J2＞0) arranged in nonperiodic sequences are studied by trace map method. For Glauber dynamics, it is found that the dynamical critical exponent z=1+J1 /J2 for the Fibonacci, general Fibonacci (e.g., silver-mean, copper-mean), and period-doubling ferromagnetic Ising chains. The applicability of the trace map method and the origin of the nonuniversality are briefly discussed.[S1063-651X (97) 05007-1]