A lubricating oil composition comprising at least 50 percent by mass, based on the mass of the composition of an oil of lubricating viscosity and 0.01 to 25 percent by mass, based on the mass of the composition of a polymer comprising units (a) and one or both units (b) and (c): —N(COR1)(CH2)x—  (a) —NH(CH2)y—  (b) —N(CH2CH2-k(CH3)kCOOR2)(CH2)z   (c) where the total number (n) of units (a), (b) and (c) is an integer between 4 and 500; wherein x, y and z are independently 2 or 3; wherein k is zero or 1. The polymer shows good solubility in the lubricating oil and provides friction modification. A method of synthesising a polymer is also disclosed.