Electron spin resonance (ESR) dating of fossil bones from the Caune de l'Arago site was attempted. Archaeological dose determined by ESR varies from sample to sample by a factor of ten according to its uranium content. Activities of ²³⁸U, ²³⁴U, ²³⁰h, ²²⁶Ra, ²²²Rn, ²¹⁰Pb, ²³¹Pa, ²²⁸Ra, ²²⁸Th, and ⁴⁰K are measured by non-destructive gamma-ray spectrometry. Growth of ²³⁰Th and ²³¹Pa from uranium in bone, escape of ²²⁶Ra and ²²²Rn from bone and soil, effect of water content, attenuation of beta and gamma rays in the sample, and distribution of uranium in fossil bone are discussed. An equation to calculate annual dose-rate is proposed with the assessment of the factors used in this calculation. -- AATA