The phase fluctuations and higher order fluctuations in odd and even coherent states have been discussed via the measured phase operators introduced by S. M. Barnett and D. T. Pegg. Based on the uncertainty relation and higher order uncertainty relation, two kinds of definitions of squeezing and higher order squeezing for the measured phase operators are introduced. Using these definitions, the squeezing and higher order squeezing of measured phase operators in odd and even coherent states have been studied.