A complete qualitative study of the dynamics of string cosmologies is prese
nted for the class of isotopic curvature universes. These models are of Bia
nchi types I, V and IX and reduce to the general class of Friedmann-Roberts
on-Walker universes in the limit of vanishing shear isotropy. A non-trivial
2-form potential and cosmological constant terms are included in the syste
m. In general, the 2-form potential and spatial curvature terms are only dy
namically important at intermediate stages of the evolution. In many of the
models, the cosmological constant is important asymptotically and anisotro
py becomes dynamically negligible. There also exist bouncing cosmologies.