A number of properties of certain living embryonic tissues can be explained by considering them as liquids. Tissue fragments left in a shaker bath round up to form spherical aggregates, as do liquid drops. When cells comprising two distinct embryonic tissues are mixed, typically a nucleation-like process takes place, and one tissue sorts out from the other. The equilibrium configurations at the end of such sorting out phenomena have been interpreted in terms of tissue surface tensions arising from the adhesive interactions between individual cells. In the present study we go beyond these equilibrium properties and study the viscoelastic behavior of a number of living embryonic tissues. Using a specifically designed apparatus, spherical cell aggregates are mechanically compressed and their viscoelastic response is followed. A generalized Kelvin model of viscoelasticity accurately describes the measured relaxation curves for each of the four tissues studied. Quantitative results are obtained for the characteristic relaxation times and elastic and viscous parameters. Our analysis demonstrates that the cell aggregates studied here, when subjected to mechanical deformations, relax as elastic materials on short time scales and as viscous liquids on long time scales.