Spiking neural networks, the most realistic artificial representation of biological nervous systems, are promising due to their inherent local training rules that enable low-overhead online learning, and energy-efficient information encoding. Their downside is more demanding functionality of the artificial synapses, notably including spike-timing-dependent plasticity, which makes their compact efficient hardware implementation challenging with conventional device technologies. Recent work showed that memristors are excellent candidates for artificial synapses, although reports of even simple neuromorphic systems are still very rare. In this study, we experimentally demonstrate coincidence detection using a spiking neural network, implemented with passively integrated metal-oxide memristive synapses connected to an analogue leaky-integrate-and-fire silicon neuron. By employing spike-timing-dependent plasticity learning, the network is able to robustly detect the coincidence by selectively increasing the synaptic efficacies corresponding to the synchronized inputs. Not surprisingly, our results indicate that device-to-device variation is the main challenge towards realization of more complex spiking networks.