Micromechanical properties of biological cells are crucial for cells functions. Despite extensive study by a variety of approaches, an understanding of the subject remains elusive. We conducted a comparative study of the micromechanical properties of cultured alveolar epithelial cells with an oscillatory optical tweezer-based cytorheometer. In this study, the frequency-dependent viscoelasticity of these cells was measured by optical trapping and forced oscillation of either a submicron endogenous intracellular organelle (intra-cellular) or a 1.5microm silica bead attached to the cytoskeleton through trans-membrane integrin receptors (extra-cellular). Both the storage modulus and the magnitude of the complex shear modulus followed weak power-law dependence with frequency. These data are comparable to data obtained by other measurement techniques. The exponents of power-law dependence of the data from the intra- and extra- cellular measurements are similar; however, the differences in the magnitudes of the moduli from the two measurements are statistically significant.