Inelastic $\ensuremath{\alpha}$-scattering experiments have been performed on $^{144}\mathrm{Sm}$ and $^{208}\mathrm{Pb}$ at ${E}_{\ensuremath{\alpha}}=96$ MeV over the angular range $3\ifmmode^\circ\else\textdegree\fi{}<~{\ensuremath{\theta}}_{L}<~8\ifmmode^\circ\else\textdegree\fi{}$. It is apparent that the isoscalar giant resonance in these nuclei consists of at least two broad components. The angular distribution for one component ($^{144}\mathrm{Sm}$ ${E}_{x}\ensuremath{\sim}12.4$ MeV, $^{208}\mathrm{Pb}$ ${E}_{x}\ensuremath{\sim}11.0$ MeV) is well described as $E2$, while that for other component ($^{144}\mathrm{Sm}$ ${E}_{x}\ensuremath{\sim}15.1$ MeV, $^{208}\mathrm{Pb}$ ${E}_{x}\ensuremath{\sim}13.7$ MeV) is well described by an $E0$ excitation exhausting approximately 100% of the $E0$ energy-weighted sum rule.