Axial velocity measurements in the die entry region of a capillary rheometer using a laser Doppler anemometer and a data logging system are reported for a Newtonian silicone oil and a highly elastic polymer solution under low Reynolds number flow conditions(NRe<1).For the silicone oil, major velocity rearrangements occur within one diameter distance upstream and the velocity distribution is independent of Reynolds number and dieL/Dratio within the range investigated. For the polymer solution, the stable converging flow field is characterized by a constant Deborah number,NDe=0.030.The axial velocity distribution becomes unsymmetric atNRe′=4.25×10−3followed by the development of spiralling instabilities at higher values ofNRe′.The site of initiation of the instabilities is at the die entry plane or downstream in the die land region.