It is shown that the joint behaviour of n counting processes can be used fo
r description of neuronal spike generation in a system of n neurons with va
rious synaptic links. This multidimensional process is suggested as a model
of neuronal activity evoked by either a homogeneous or an inhomogeneous st
imulus during a short time period. Several situations are considered, mainl
y the joint activity of pairs of neurons. The probability generating functi
ons of the process are obtained for different kinds of intensity functions.
The first and second moments of the process are provided as a tool for pot
ential comparison of the model with experimental data.