Order statistics arising from exponentiated gamma (EG) distribution are considered. Closed from expressions for the single and double moments of order statistics are derived. Measures of skewness and kurtosis of the probability density function of the rth order statistic for different choices of r, n and /theta are presented. Recurrence relations between single and double moments of rth order statistics are obtained. Single moment generating function (MGF) is derived in closed form. Also, we establish several recurrence relations between single MGF.