To establish laser-tracking microrheology (LTM) as a new technique for quantifying cytoskeletal mechanics, we measure viscoelastic moduli with wide bandwidth (5 decades) within living cells. With the first subcellular measurements of viscoelastic phase angles, LTM provides estimates of solid versus liquid behavior at different frequencies. In LTM, the viscoelastic shear moduli are inferred from the Brownian motion of particles embedded in the cytoskeletal network. Custom laser optoelectronics provide sub-nanometer and near-microsecond resolution of particle trajectories. The kidney epithelial cell line, COS7, has numerous spherical lipid-storage granules that are ideal probes for noninvasive LTM. Although most granules are percolating through perinuclear spaces, a subset of perinuclear granules is embedded in dense viscoelastic cytoplasm. Over all time scales embedded particles exhibit subdiffusive behavior and are not merely tethered by molecular motors. At low frequencies, lamellar regions (820 +/- 520 dyne/cm(2)) are more rigid than viscoelastic perinuclear regions (330 +/- 250 dyne/cm(2), p < 0.0001), but spectra converge at high frequencies. Although the actin-disrupting agent, latrunculin A, softens and liquefies lamellae, physiological levels of F-actin, alone (11 +/- 1.2 dyne/cm(2)) are approximately 70-fold softer than lamellae. Therefore, F-actin is necessary for lamellae mechanics, but not sufficient. Furthermore, in time-lapse of apparently quiescent cells, individual lamellar granules can show approximately 4-fold changes in moduli that last >10 s. Over a broad range of frequencies (0.1-30, 000 rad/s), LTM provides a unique ability to noninvasively quantify dynamic, local changes in cell viscoelasticity.