The factors determining the position resolution of continuous crystal based position sensitive scintillation gamma detectors are discussed. The key factors are the position functions which give the relation between the coordinates of the point of interaction (POI) and the responses of the photodetectors reading out of the scintillator. The physical phenomena limiting the position resolution are the statistical fluctuation of the detected photons and the electronic noise. For the standard deviation of the POI coordinates simple relations are deduced. It has been established that the contributions of both the statistical fluctuation and the noise to the standard deviation of the POI coordinates are inversely proportional to the square root of the detected photon numbers and the measure of these contributions can be characterised with the position resolution coefficients deduced from the position functions. A detailed discussion of the effect of the scintillator and photodetector characteristics is also given. As an example, calculations for the resolution coefficients in the case of the solid angle method with a chosen scintillator photodetector arrangement are given. The results show that the resolution coefficients as a function of the POI coordinates vary in a wide range. With realistic practical data and using almost the largest value for the resolution coefficients similar or better position resolution can be reached with continuous crystal than with a pixellated one.