Gaussian mixture models (GMMs) are recently employed to provide a robust technique for speaker identification. The determination of the appropriate number of Gaussian components in amodel for adequate speaker representation is a crucial but difficult problem. This number is in fact speaker dependent. Therefore, assuming a fixed number of Gaussian components for all speakers is not justified. In this paper, we develop a procedure for roughly estimating the maximum possible model order above which the estimation of model parameters becomes unreliable. In addition, a theoretical measure, namely, a goodness of fit (GOF) measure is derived and utilized in estimating the number of Gaussian components needed to characterize different speakers. The estimation is carried out by exploiting the distribution of the training data for each speaker. Experimental results indicate that the proposed technique provides results comparable to other well-known model selection criteria like the minimum description length (MDL) and the Akaike information criterion (AIC).