Clear-sky Direct Normal Irradiance (DNI) is the solar power received at ground level per unit of area, at a specific location, under cloud-free conditions. Regarding Concentrating Solar Power (CSP) technologies, such conditions mean that there is no cloud between the Sun and the observer, i.e. the solar field. Since clear sky defines the nominal operating conditions of CSP plants, real-time estimates and forecasts of clear-sky DNI are key information for power plant operators tasked with the management of those plants. So, the present paper focuses first on a new algorithm for the real-time detection of clear-sky situations from DNI measurements. This algorithm makes use of the last-known clear-sky situation and requires the maximum speed at which the atmosphere becomes opaque to be evaluated. The paper also focuses on an efficient approach to the real-time assessment of clear-sky DNI. This approach combines the model developed by Ineichen and Perez with a persistence of atmospheric turbidity, taking advantage of the fact that changes in this quantity are relatively small throughout the day in comparison to changes in DNI, even when the sky is free of clouds. Performance is evaluated via a comparative study, in which empirical models are included, using one-minute data from two sites (Golden, USA, and Perpignan, France). MAE and RMSE are lower than 10 W m(-2) and 21 W m(-2), respectively. The same approach is capable of providing accurate intraday forecasts of clear-sky DNI. It has proven to be the best compromise between accuracy and complexity (reference is a persistence of DNI) among the considered approaches, including neuro-fuzzy approaches. For a forecast horizon of 5 h,MAE similar or equal to 30 W m(-2) and RMSE similar or equal to 37 W m(-2).