An irreversible loss of subcutaneous adipose tissue in patients after tumor removal or deep dermal burns makes soft tissue engineering one of the most important challenges in biomedical research. The ideal scaffold for adipose tissue engineering has yet not been identified though biodegradable polymers gained an increasing interest during the last years. In the present study we synthesized two novel biodegradable polymers, poly(ε-caprolactone-co-urethane-co-urea) (PEUU) and poly[(L-lactide-co-ε-caprolactone)-co-(L-lysine ethyl ester diisocyanate)-block-oligo(ethylene glycol)-urethane] (PEU), containing different types of hydrolytically cleavable bondings. Solutions of the polymers at appropriate concentrations were used to fabricate fleeces by electrospinning. Ultrastructure, tensile properties, and degradation of the produced fleeces were evaluated. Adipose-derived stem cells (ASCs) were seeded on fleeces and morphology, viability, proliferation and differentiation were assessed. The biomaterials show fine micro- and nanostructures composed of fibers with diameters of about 0.5 to 1.3 µm. PEUU fleeces were more elastic, which might be favourable in soft tissue engineering, and degraded significantly slower compared to PEU. ASCs were able to adhere, proliferate and differentiate on both scaffolds. Morphology of the cells was slightly better on PEUU than on PEU showing a more physiological appearance. ASCs differentiated into the adipogenic lineage. Gene analysis of differentiated ASCs showed typical expression of adipogenetic markers such as PPARgamma and FABP4. Based on these results, PEUU and PEU meshes show a promising potential as scaffold materials in adipose tissue engineering.