Implementation of a correlation-based learning rule, Spike-Timing-Dependent-Plasticity (STDP), for asynchronous neuromorphic networks is demonstrated using `memristive' nanodevice. STDP is performed using locally available information at the specific moment of time, for which mapping to crossbar-based CMOS-Nano architectures, such as CMOS-MOLecular (CMOL), is done rather easily. The learning method is dynamic and online in which the synaptic weights are modified based on neural activity. The performance of the proposed method is analyzed for specifically shaped spikes and simulation results are provided for a synapse with STDP properties.