N=2 Chiral Bosons in Superspace

We explore N=2 chiral bosons in (2,2), (2,0) and (0,2) superspaces. We start with a manifestly covariant (2,2) description in the Ogievetssky-Sokatchev geometric approach and then, by fixing gauges with respect to local Siegel's transformations, obtain previously unknown (2,0) and (0,2) actions, The anomalous N=2 Feigin-Fuchs term in a (2,0) superfield form is presented. We introduce a Liouville representation for the Feigin-Fuchs-term-modified N=0, N=1 and N=2 chiral bosons, thus demonstrating the relevance of these systems to the two-dimensional (super)gravity and non-critical (super)string theories.