An important contribution to neural circuit oscillatory dynamics is the ongoing activation and inactivation of hyperpolarization-activated currents (/h). Network synchrony dynamics play an important role in the initial processing of odor signals by the main olfactory bulb (MOB) and accessory olfactory bulb (AOB). In the mouse olfactory bulb, we show that /h is present in granule cells (GCs), the most prominent inhibitory neuron in the olfactory bulb, and that /h underlies subthreshold resonance in GCs. In accord with the properties of /h, the currents exhibited sensitivity to changes in extracellular K+ concentration and ZD7288 (4-ethylphenylamino-1,2-dimethyl-6-methylaminopyrimidin chloride), a blocker of /h. ZD7288 also caused GCs to hyperpolarize and increase their input resistance, suggesting that /h is active at rest in GCs. The inclusion of cAMP in the intracellular solution shifted the activation of /h to less negative potentials in the MOB, but not in the AOB, suggesting that channels with different subunit composition mediate /h in these regions. Furthermore, we show that mature GCs exhibit /h-dependent subthreshold resonance in the theta frequency range (4–12 Hz). Another inhibitory subtype in the MOB, the periglomerular cells, exhibited /h-dependent subthreshold resonance in the delta range (1–4 Hz), while principal neurons, the mitral cells, do not exhibit /h-dependent subthreshold resonance. Importantly, /h size, as well as the strength and frequency of resonance in GCs, exhibited a postnatal developmental progression, suggesting that this development of /h in GCs may differentially contribute to their integration of sensory input and contribution to oscillatory circuit dynamics.