The flow patterns of oil/water two-phase flow in vertical upward pipes have been characterized by the analysis of LZ complexity and fluctuation complexity measures using the conductance time series fluctuating signals. It is shown that both complexity measures have little changes with oil-in-water flow pattern variations for flow conditions of 61%/spl les/K/sub w//spl les/91% and irregular sudden changes to the transitional flow pattern variations for 51% of water cut (K/sub w/). We conclude that the two complexity measures are sensitive 'indicators' of flow pattern variations and the analysis method of complexity is an useful supplementary diagnostic tool for oil/water two phase flow patterns identification.