  Low-energy electron collisions with O$_2$ molecules are studied using the
fixed-bond R-matrix method. In addition to the O$_2$ ${X}^3\Sigma_{g}^-$ ground
state, integrated cross sections are calculated for elecron collisions with the
${a}^1\Delta_{g}$ and ${b}^1\Sigma_{g}^+$ excited states of O$_2$ molecules. 13
target electronic states of O$_2$ are included in the model within a valence
configuration interaction representations of the target states. Elastic cross
sections for the ${a}^1\Delta_{g}$ and ${b}^1\Sigma_{g}^+$ excited states are
similar to the cross sections for the ${X}^3\Sigma_{g}^-$ ground state. As in
case of excitation from the ${X}^3\Sigma_{g}^-$ state, the O$_2^-$ $\Pi_u$
resonance makes the dominant contribution to excitation cross sections from the
${a}^1\Delta_{g}$ and ${b}^1\Sigma_{g}^+$ states. The magnitude of excitation
cross sections from the ${a}^1\Delta_{g}$ state to the ${b}^1\Sigma_{g}^+$
state is about 10 time larger than the corresponding cross sections from the
${X}^3\Sigma_{g}^-$ to the ${b}^1\Sigma_{g}^+$ state. For this
${a}^1\Delta_{g}$ $\to$ ${b}^1\Sigma_{g}^+$ transition, our cross section at
4.5 eV agrees well with the available experimental value. These results should
be important for models of plasma discharge chemistry which often requires
cross sections between the excited electronic states of O$_2$.
