A method for producing a capillary comprises the steps of providing first a capillary having a uniform inner width throughout its length, introducing then an etchant into the capillary, and producing a temperature gradient over the length of the capillary in such a way that a temperature-controlled increased expansion of the inner width of the capillary will take place during the etching process in the heated region thereof. A capillary produced in this way is excellently suitable for use in an electrophoresis device.