<p>Production takes place in complex networks. An important question is how the efficiency of the whole network is related to that of the individual production units forming the network. A general network production theory with following characteristics is developed. Analysed networks may possess arbitrary structures with units whose technologies may be non-convex and even discrete. The theory generalises Koopmans’ linear activity analysis based on similar underlying modelling features and fundamental assumptions. The modelling approach is more suitable for analysing networks than common ones. Methods of efficiency measurement known from network data envelopment analysis are integrated into the theory. It is shown that calculating an overall efficiency score for a network as average of individual scores of its units is inappropriate. The relationship between the efficiency of a network activity and that of subsystems and units strongly depends on the extent of which the individual production units are free to choose their input and output quantities, i.e. whether the network is loose or tied. Especially in cases where flows of intermediate products are constrained instead of freely disposable, the explicit modelling of their overproduction helps to analyse their influence on efficiency scores.</p>