Networks of hippocampal interneurons, with pyramidal neuronspharmacologically disconnected, can generate gamma-frequency(20 Hz and above) oscillations. Experiments and models have shownhow the network frequency depends on excitation of the interneurons,and on the parameters of GABA{\rm A}-mediated IPSCs betweenthe interneurons (conductance and time course). Herewe use network simulations to investigate how pyramidal cells, connected tothe interneurons and to each other throughAMPA-type and/or NMDA-type glutamatereceptors, might modify the interneuron network oscillation. With orwithout AMPA-receptor mediated excitation of the interneurons, the pyramidal cells and interneurons fired in phaseduring the gamma oscillation. Synaptic excitation of the interneuronsby pyramidal cellscaused them to fire spike doublets or short bursts at gammafrequencies, thereby slowing the population rhythm.Rhythmic synchronized IPSPs allowed the pyramidal cells toencode their mean excitation by their phase of firing relativeto the population waves.Recurrent excitation between the pyramidal cells couldmodify the phase of firing relative to the population waves.Our model suggests that pools of synaptically interconnectedinhibitory cells are sufficient to produce gamma frequency rhythms,but the network behavior can be modified by participation ofpyramidal cells.