Extensive researches on nano-composite materials submitted to shear flow or extensional flow, have been motivated by their spectacular rheological behavior and vast industrial applications (deposition, ultrafiltration, extrusion, etc.). Indeed, these materials under extensional flow can exhibit time dependent viscoelastic properties. Instabilities such as localization, phase separation, segregation, can occur which are not well understood. The scientific objective of this research is to elucidate the relationship between the extensional flow properties (strain and stress fields) and the dynamics of the induced structures (orientation, aggregation, phase transition, etc.). The nano-composite materials studied are composed of sepiolite clay particles (rigid rods 1 micrometer long and 0.010 micrometers in diameter) in a water-soluble polymer, polyethylene oxide. The trajectory of the strain field within the sample volume has been well characterized by particle imaging velocimetry, in order to apply pure extensional flows in the desired extensional rate and viscosity domains. A new extensional flow device developed at the "Laboratoire de Rhéologie", has allowed to combine extensional flow with SAXS on ID02 at the ESRF. Time-resolved information has been obtained on the orientation dynamics of the fibers in the polymer matrix. Analysis of extensional transient and steady state regimes revealed the main characteristics of the extensional flow of these nano-composite suspensions. Under steady states, the fibers are aligned along the extensional direction. The evolution of the orientation order parameter versus strain rate has allowed defining the rate of organization of the fibers at increasing extensional flow rates. Under transient states, time evolution of the order parameter permitted to identify the time scales at which the fibers get aligned in the extensional field and the time scales over they relax in the polymer matrix.