The geometric process (GP) has been widely used for modeling failure and repair time sequences of repairable systems. The GP is mathematically tractable but restrictive in reliability applications since it actually assumes that the mean function of inter-failure times sequence asymptotically decreases to zero; and the mean function of successive repair times sequence asymptotically increases to infinity. This is generally unrealistic from an engineering perspective. This paper presents three extended GP models for modeling reliability deterioration and improvement (or growth) process. The extensions maintain the advantage of mathematical tractability of GP model. Their usefulness and appropriateness are illustrated with three real-world examples.