A first version of a neurobiologically inspired neural network model for speech and language processing using a spiking neuron approach is introduced here. This model uses basic neural circuit elements for building up a large-scale brain model (i.e., elements for long-term and short-term memory, elements for activating and forwarding information (items) as neural states, elements for cognitive and sensorimotor action selection, elements for modeling binding of items, etc.). The resulting model architecture indicates three dense neural network modules, i.e., a module for lexical, for syntactic, and for semantic processing. Moreover, the model gives a detailed specification of the neural interaction interfaces between these modules. This large-scale model is capable of parsing syntactic simple but non-trivial sentences of Standard German and it clearly exemplifies the temporal-parallel as well as the hierarchical-sequential neural processes typically appearing in speech processing in the brain.