Spiking Neural Networks (SNNs) are gaining great attention for their energy-efficient and event-driven properties in neuromorphic computing. Despite this, the efficient training of deep SNNs encounters challenges in gradient calculation, primarily due to the non-differentiability of their binary spike-generating activation functions. The widely used surrogate gradient (SG) method, along with the application of back-propagation through time (BPTT), has shown considerable effectiveness. However, BPTT's unfolding and back-propagating along the computation graph requires storing intermediate information at all time-steps, resulting in huge memory consumption and failing to meet online requirements. In this work, we employ the neuronal dynamics-based temporal dependency/sensitivity in the gradient computation and propose Neuronal Dynamics-based Online Training (NDOT) for SNNs. The NDOT enables forward-in-time learning by decomposing the full gradient into temporal gradient and spatial gradient. To clarify the intuition behind NDOT, we employ the Follow-the-Regularized-Leader (FTRL) algorithm. FTRL explicitly utilizes historical information and addresses limitations in instantaneous loss. Our proposed NDOT method accurately captures temporal dependencies through neuronal dynamics, functioning similarly to FTRL's explicit use for capturing historical information. Experiments on CIFAR-10, CIFAR-100, and CIFAR10-DVS demonstrate the superior performance of our NDOT method on large-scale static and neuromorphic datasets within a small number of time steps.