Polymers are little considered at the moment, in the wide domain of micro- and nano- technologies. They present however certain remarkable properties by comparison with the materials used in microelectronics. For example their flexibility and their lightness allow thinking to polymers as flexible supports for microelectronic components. Besides, they offer solutions for assembling various materials.This study concerns exactly these two items. First of all, we studied bonding mechanisms implied in the assembly of silicon wafers via polymer layers. Then we proposed models for mechanism of single-crystalline layer transfers onto polymers. The mechanical properties of the considered materials (mainly single-crystalline silicon and glassy or rubber polymers) as well as their thicknesses can vary on several orders of magnitude according to the application.The originality of the study is to determine favorable experimental configurations, by simple mechanical models developed from scale laws, and to realize demonstrators. The heart of our study concerns the transfer of single-crystalline layers as thin as about hundred nanometers onto polymers by tuning of the Smart-CutTM technology (based on ion implantation and splitting for transfer). By comparison with a standard configuration of this technology, we studied the impact of the specific mechanical properties of polymers (glassy or rubber types). The methods in scale laws allowed us proposing transfer mechanisms, from the nanometer scale up to the macroscopic one. Finally we reported on a realization of micro-technology devices, made in and on single-crystalline thin silicon membranes. The stacked structures, consisting in silicon membranes thick of a few micrometers supported by polymer films, may be considered as very flexible structures.