On complete pseudoconvex Reinhardt domains in ℂ², we show that there is no nonzero Hankel operator with anti-holomorphic symbol that is Hilbert-Schmidt. In the proof, we explicitly use the pseudoconvexity property of the domain. We also present two examples of unbounded non-pseudoconvex domains in ℂ² that admit nonzero Hilbert-Schmidt Hankel operators with anti-holomorphic symbols. In the first example the Bergman space is finite dimensional. However, in the second example the Bergman space is infinite dimensional and the Hankel operator Hz¯₁z¯₂ is Hilbert-Schmidt., Mehmet Çelik, Yunus E. Zeytuncu., and Obsahuje bibliografii