The atmospheric scintillation of stars is the main reason why the ground-based photometry of astronomical objects has limited accuracy. This becomes particularly noticeable for a variability study with amplitudes of the order of thousandths of stellar magnitude or less. We examine the problem of colour scintillation (i.e. fluctuations of the difference between light intensities measured simultaneously in two different photometric bands). We derive the relations between the colour scintillation power (index) and the atmospheric turbulence, telescope diameter and the characteristics of the photometric channels. Asymptotic dependences for large telescopes (1–10 m) are obtained, which allow us to predict the value of the colour scintillation for a particular telescope and detector. It is shown that the colour scintillation index is ∝ D−3 for measurements with both short (milliseconds) and long (seconds) exposures. We estimate the impact of the atmospheric dispersion, which amplifies colour scintillation away from the zenith. We show that colour scintillation in the long-exposure regime depends strongly on the wind direction in the upper atmosphere.