An eyeglass lens processing apparatus includes: a controller that controls a second driver for rotating lens chucks for chucking an eyeglass lens and a third driver for changing an axis-to-axis distance between an axis of a processing tool and an axis of the lens chucks so that a processing load falls below an allowable value; and a processing mode selector that selects one of a first processing mode in which the allowable value is set to be high, and a second processing mode in which the allowable value is set to be low so as to suppress axis deviation when the lens having a surface slipping readily is processed. The controller controls the first driver so that a second chucking pressure of the lens chucks when the second processing mode is selected is smaller than a first chucking pressure of the lens chucks when the first processing mode is selected.
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