The dynamics of linear and regular star polymers in a good solvent and in the Theta state is investigated theoretically considering the viscoelastic and the oscillatory flow birefringence response under an alternating shear deformation. We show that in a good solvent the phase angles of the viscoelastic and of the birefringence response are different. The physical reason of this difference is that viscoelasticity depends on the orientation of the chain stresses with the applied deformation, whereas birefringence measurements probe the orientation of the chain bonds. Only in the phantom chain the two orientations are the same, whereas this is no more true in a good solvent because of the long-range intramolecular interactions. Moreover, the phase angles show a maximum in the case of stars at omega congruent to 1/tau(1), where omega is the applied frequency and tau(1) the longest relaxation time, that is strictly related to a shoulder in the imaginary part of the complex modulus. The reasons of this feature, which is absent in linear chains, are discussed in connection with the discrete spectrum of relaxation times.