  We construct symplectic structures on roughly half of all equal rank
biquotients of the form $G//T$, where $G$ is a compact simple Lie group and $T$
a torus, and investigate Hamiltonian Lie group actions on them. For the
Eschenburg flag, this action has similar properties as Tolman's and Woodward's
examples of Hamiltonian non-K\"ahler actions. In addition to the previously
known K\"ahler structure on the Eschenburg flag, we find another K\"ahler
structure on a biquotient $\mathrm{SU}(4)//T^3$.
