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The empirically observed inter-spike interval (ISI) patterns in neuronal dynamics exhibit unimodal and bimodal behavior. The widely studied IF and LIF models are known to display only unimodal ISI distribution. A challenging problem in modeling of neuronal dynamics is to understand mechanism which can generate the empirically observed ISI patterns. A new neuronal model incorporating distributed delay (NMDD), proposed by Karmeshu, Varun, and Kadambari has been investigated in greater details for gamma distributed memory kernels with weak and strong delays. The underlying dynamics of membrane potential in subthreshold regime may result in bimodality of ISI distribution. It is found as the mean of the delay kernel exceeds a critical value, the ISI distribution makes a transition from unimodal to bimodal. Extensive simulation studies reveal that different empirically observed ISI patterns can be generated and interesting behavior is observed when excitatory and inhibitory rates of EPSP and IPSP processes are close to each other. This investigation suggests the important role played by distributed delays in neuronal dynamics.