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Gaussian mixture models, which assume a Normal distribution for each component, are popular in antibody (or serological) data analysis to help determining antibody-positive and antibody-negative individuals. In this work, we advocate using finite mixture models based on Skew-Normal and Skew-t distributions for serological data analysis. These flexible mixing distributions have the advantage of describing right and left asymmetry often observed in the distributions of known antibody-negative and antibody-positive individuals, respectively. We illustrate the application of these alternative mixture models in a data set on the role of human herpesviruses in the Myalgic Encephalomyelitis/Chronic Fatigue Syndrome.