The amplitude of the electron spin resonance (ESR) peak at g = 2.0018 for hydroxyapatite of fossil tooth enamel can be used to measure the acquired radiation dose (AD) and thus the time (T) since burial of the tooth in a sediment. No significant fading or saturation occurs up to at least 1 Ma, permitting dating of middle Pleistocene deposits. AD is determined by the additive-dose method, using a sufficiently large modulation amplitude to avoid the interference of organic free radicals, and a logarithmic transformation of the ESR intensity to correct for saturation effects. AD increases through time as a result of (1) constant irradiation by U, K, and Th in the surrounding sediment and by cosmic rays; (2) external irradiation by beta particles from U in the dentine; and (3) alpha and beta particles from U in the enamel. We derive an expression for AD(T) taking into account (1) approach to equilibrium between U and its long-lived daughters; and (2) T-dependent (early or linear) uptake of U by dentine or cement and by enamel, as well as the constant environmental radiation sources. T is determined by iteratively solving this expression to obtain the observed AD. An example is given of the dating of an elephant tooth from a preglacial deposit in Alberta: the calculated age is consistent with assignment to isotope stages 5c–5e.