无恒变形虫最早於1916年由美國生物學家阿薩·阿圖·沙弗(德语:Asa Arthur Schaeffer)描述發表,當時被歸入變形蟲屬中,名為Amoeba dubia[2],1926年沙弗認為本種與該屬其他物種有所差異,而將其同屬的囊多卓变虫[註 1]一起歸入新屬多卓变虫属(Polychaos),並以本種為該屬的模式種[1]。
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