Abstract: The invention relates to a pump for biological fluids, for example for blood transference by pump. The pump according to the invention comprises a housing (1) in which there are placed at least one resilient tube (3) for passing biological fluid, and an operating head (5) rotated in the direction of fluid transference and including at least one roller member (6) to bear against the tube (3), said roller member (or each roller member) comprising at least two rollers (7,8) positioned in series so that the roller (7) of said roller member which is preceding in the direction of the operating head rotation allows greater tube (3) aperture than does the roller (8) of the same member (6) that follows. The pump has simple and convenient means for adjusting the degree of compressing the tube (3) by the rollers (7,8) and ensures blood transfusion causing practically no damage to the blood cells.