Recent studies on the giant monopole resonance (GMR) and the giant quadrupole resonance (GQR) in /sup 144/Sm and /sup 208/Pb using the ..cap alpha..-scattering performed at RCNP are summarized. The observed angular range covered 1.6/sup 0/ -- 7/sup 0/ with a coupled system of a dipole and a triplet quadrupole magnet. The incident energy was changed from 84 to 119 MeV. The resonance shapes and energy-weighted sum-rule strengths of the GMR and the GQR were reliably deduced as a function of incident energy. The quadrupole strength of --20% was found in the GMR region. The observed excitation function of the GMR was compared with the DWBA calculation, in which the Satchler's Version I was used as a form factor representing the compressional motion of the nucleus. It was found that the experimental excitation function of the GMR shows steeper decrease as lowering the incident energy than the DWBA prediction whereas that of the GQR is successfully described by the DWBA. This suggests that examination of the model describing the GMR is necessary.