Abstract: We explore a fishery targeting the mature part of a stock, while by catching the immature part. Both targeted catch and bycatch may have positive market values. Cost of effort is supposed to be a function of the selection properties of the fishing gears. Mature fish is assumed to cannibalise on the immature part of the stock. A bioeconomic model of the problem is set up and it is shown that the model possesses a unique nontrivial stable equilibrium and moreover that both cannibalism and catch act as stabilising factors. Necessary conditions for a bioeconomic optimum are also provided. The model is applied on the Northeast Arctic cod stock where time series of stock biomasses, catches and fishing mortality rates covering the period 1946-2000 have been used to estimate the model parameter values. The economic parameters have been estimated on the basis of previous open access to the fishery, assuming bioeconomic equilibrium. It is shown that bioeconomic optimum could not be obtained at any discount rate, without reducing the rate of fishing mortality, first of all on the mature part of the cod population.