My lecture on bifurcation and stability of solutions which branch from forced T-periodic solutions is based on the recent work of G. IOOSS and myself [1] and on my forthcoming paper on factorization theorems [2]. In general, forced T-periodic solutions bifurcate into subharmonic solutions with a fixed period τ(τ=nT; n=1,2,3,4) independent of the amplitude or into a torus [1,3,4,5,6] containing solutions whose analytic properties are not yet fully understood. The subharmonic bifurcating solutions with n=1 are the T-periodic equivalent of a symmetry-breaking bifurcation of steady solutions with other steady solutions. The symmetry breaking flower instability of the axisymmetric climb of a viscoelastic fluid on an oscillating rod [7] which is shown in the movie “Novel Weissenberg effects” by G. S. BEAVERS and myself is one example of such a symmetry breaking T-periodic bifurcation. The solutions on the torus are very roughly the T-periodic equivalent of a Hopf bifurcation, of a steady solution into a periodic solution; like the Hopf bifurcation the solutions on the torus possess frequencies which depend on the amplitude but in the nonautonomous, T-periodic case the variation of these frequencies need not be smooth. A good example of smooth variation of frequencies on a two-dimensional torus appears to describe the observations of SWINNEY, FENSTERMACHER and GOLLUB [8, 9] of the oscillatory regimes of flow which follow wavy vortices in the Taylor problem when the Reynolds number is increased.