Abstract: The relationship between readings on two instruments may be represented by a linear functional relationship with errors of observation in both variables. This study describes a method of fitting the relationship between the two circular variables and the replicate observations are available. Maximum likelihood estimates are used and it is shown that the closed-form expression for the estimators are not available and the estimates may be obtained iteratively by choosing a suitable initial value. The model is illustrated with an application to the analysis of the wave and wind direction data recorded by two different instruments and assuming the pseudo-replicates based on time have been obtained from this unreplicated circular data.