Attrition rates and mean transport velocities of coarse fluvial sediments averaged over long periods of time (100 a) are yet to be fully quantified. A knowledge of long-term transport rates would allow us to predict the response of fluvial systems to changes in external conditions, while determining clast attrition rates would improve our understanding of fluvial abrasion processes. The concentration of terrestrial cosmogenic nuclides (TCNs) in boulders can be modified during river transport by attrition and temporary exposure, which are two competing processes. In order to evaluate the potential of TCNs to quantify these processes, a stochastic model of TCN concentration evolution in clasts of different sizes is developed from exhumation on a hillslope to a sampling point in a river. The model includes shallow landslides or movement in a regolith and episodic transport of clasts in a sediment layer on the river bed. We study the downstream evolution of TCN concentrations for a population of clasts sourced from a localized TCN-rich lithology on a hillslope. When attrition is strong, the model predicts that the variance and maximum of TCN concentrations decrease downstream. Such a trend is possible only if the dominant hillslope erosion corresponds to shallow landslides. Natural variability of hillslope processes can hamper the trend. A way to limit the scatter is to sample the biggest clasts. On the contrary, if clast attrition is small and river transport slow, TCN concentrations increase downstream. In this case, combining the TCN concentrations of clasts gathered at several river stations should provide a method to estimate their mean transport rate. Our results offer guidelines to interpret the downstream evolution of TCN concentration in pebbles and at the surface of boulders.