The time-dependent, local microbuckling of multilayered viscoelastic media is modeled with emphasis on bifurcation and imperfection sensitivity. The instability or 'growth-of-waviness'-type analysis is carried out for initially straight fibers (bifurcation), as well as for initially wavy fibers (imperfection-sensitivity), assuming a perfect-slip condition at the fiber-matrix interface. The concept of dominant wavelength (i.e. the fastest growing wavelength within the Fourier spectrum), previously defined for viscoelastic bifurcation (Biot, M. A. 'Mechanics of Incremental Deformations', John Wiley and Sons, Inc., New York, 1965), is extended from the single fiber analysis (Bhalerao, M. and Moon, T., On the growth-of-waviness in fiberreinforced polymer composites: viscoelastic bifurcation and imperfection sensitivity, ASME J. A&. Mechanics, in press, 1995) to multiple fiber analysis for a multilayered medium. A parametric study is presented which covers a wide range of physically relevant values. The results for the multiple fiber analysis are found to be analogous to those for single fiber analysis. The bifurcation dominant wavelength depends negligibly on matrix properties, yet highly on the applied load. On the other hand, the imperfection-sensitive dominant wavelength is predicted to depend strongly on matrix properties, while negligibly on load. The imperfection-sensitive wavelength is the one important in composites processing and in-service behavior.