ABSTRACT We study moduli of semi-stable vector bundles on non-Kahler elliptic complex surfaces and on non-Kahler principal elliptic bundles, which are Calabi-Yau type 3-folds. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction (joint work with R. Moraru, A. Halanay and G. Trautmann).