Pulsatile release of gonadotropin releasing hormone (GnRH) is crucial in the treatment of endocrine disorders related to deficiency in the episodic secretion of that hormone. In this dissertation an autonomous, implantable hormone delivery system capable of delivering GnRH in a rhythmic, pulsatile manner is under development. The device consists of a pH-sensitive hydrogel membrane, and the enzyme glucose oxidase. On implantation, physiologically available glucose diffuses through the membrane to the glucose oxidase, which converts glucose to hydrogen ion, resulting in pH drop within the device. This pH drop leads to hydrogen ion binding to the membrane, rendering it impermeable to glucose. Hydrogen ion production in the device is thus halted, and the bound hydrogen ions eventually dissociate from the membrane and diffuse into the external medium, thus restoring the initial permeability of the membrane to glucose. Under a range of conditions, oscillations in the permeability of the membrane, and consequently the release of GnRH can be achieved. Currently, the prototype device oscillates for about seven days before reverting to a steady state. In this dissertation the mechanisms underlying oscillatory behavior and reversion to steady state are investigated experimentally. A mathematical model of the device is developed to understand the events leading to oscillation and to understand the effect of experimental parameters on the dynamics of the oscillator. The effect of membrane composition on the oscillations generated is also studied.