Family is an institution that starts with the marriage of a man and a woman, based on their mutual respect, love and trust so that they spend the rest of their lives together, and that forms the smallest unit of society. The years spent together expand the family with the increasing number of children, grandchildren and relatives. However, there is a specific case that has come to take place throughout the history, which usually arises from similar causes within the family and generally leads to similar results. This case is the second marriage of the man especially in patriarchal societies, either by divorcing his first wife or by leading his married life with two wives. The second marriages, or bigamy, of men in Ancient Greece, which is today accepted as the cultural capital city of the western civilization and where generally monogamy was adopted, will be analysed through two mythological stories in two Ancient Greek tragedies. Heracles makes a second marriage for youth and beauty in Women of Trachis by Sophocles, while Jason does so for power and property in Medea by Euripides. With the husbands’ attempts to convince their wives logically albeit selfishly in the face of their wives’ reactions out of jealousy and inability to espouse these marriages and with the comments and recommendations of the chorus assuming the role of common sense and mentor of that society, these two plays reflect the approach of the Greek society of nearly 2500 years ago to bigamy or polygamy clearly. Given that theatre is the mirror of and to the society, these plays will contribute to historical, anthropological, folkloric and cultural studies, and offer a chance to make a comparison with the present time. Also, the attitude of man and woman to marriage, their role and status in it and the understanding of marriage in a patriarchal society will be analysed.