Lattice-dynamical properties of CaAlSi and SrAlSi with a similar layer structure to MgB(2) have been first investigated by both Raman-scattering and ab initio calculations. All Raman-active phonons with E' symmetry have been clearly observed for both compounds. Their line shapes are asymmetric but their linewidths are similar to 10 cm(-1), which is very narrower than that of MgB(2). In addition to the Raman-active modes, several extra peaks have been observed below 160 cm(-1). These low-energy extra modes can be assigned to the out-of-plane vibrations of Al perpendicular to Al-Si basal plane. Since these peak intensities are strongly affected by the incident energy (resonance Raman process), the electronic state is important for them. Moreover, in both crystals of CaAlSi and SrAlSi, we point out the energy difference for the different propagation directions along the c axis and the c plane, in spite of the very close wave vector to the Brillouin-zone center. This energy difference cannot be explained by a usual Raman-scattering scenario at this stage.