Ultrasonic measurements have been carried out to investigate the critical dynamics of structural and superconducting transitions due to degenerate orbital bands in iron pnictide compounds with the formula Ba(Fe1-xCox)(2)As-2. The attenuation coefficient alpha(L[110]) of the longitudinal ultrasonic wave for (C-11 + C-12 + 2C(66))/2 for x = 0.036 reveals the critical slowing down of the relaxation time around the structural transition at T-s = 65K, which is caused by ferro-type ordering of the quadrupole Ox'2-y'2 coupled to the strain e(xy). The attenuation coefficient alpha(66) of the transverse ultrasonic wave for C-66 for x = 0.071 also exhibits the critical slowing down around the superconducting transition at T-SC = 23K, which is caused by ferro-type ordering of the hexadecapole H-z(alpha)(r(i), r(j)) = O-x'y' (r(i))Ox'2-y'2(r(j)) + Ox'2-y'2(r(i))O-x'y' (r(j)) of the bound two-electron state coupled to the rotation.xy. It is proposed that the hexadecapole ordering associated with the superconductivity brings about spontaneous rotation of the macroscopic superconducting state with respect to the host tetragonal lattice.