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Tumour progression is an evolutionary process in which different clones evolve over time, leading to intra-tumour heterogeneity. Interactions between clones can affect tumour evolution and hence disease progression and treatment outcome. Intra-tumoural pairs of mutations that are overrepresented in a co-occurring or clonally exclusive fashion over a cohort of patient samples may be suggestive of a synergistic effect between the different clones carrying these mutations. We therefore developed a novel statistical testing framework, called GeneAccord, to identify such gene pairs that are altered in distinct subclones of the same tumour. We analysed our framework for calibration and power. By comparing its performance to baseline methods, we demonstrate that to control type I errors, it is essential to account for the evolutionary dependencies among clones. In applying GeneAccord to the single-cell sequencing of a cohort of 123 acute myeloid leukaemia patients, we find 1 clonally co-occurring and 8 clonally exclusive gene pairs. The clonally exclusive pairs mostly involve genes of the key signalling pathways. Author summary: Tumours typically display high levels of heterogeneity, not only between different tumours but also within a single one. Intra-tumour heterogeneity results from an evolutionary process, giving rise to different populations of cancer cells known as clones. How clones interact may affect tumour evolution, which in turn determines disease progression and treatment outcome. In practice, we may observe pairs of mutations that co-occur in clones or exclude each other more often than we would expect for a given cohort of patient samples. Exclusive pairs are suggestive that clones carrying one or the other mutation may cooperate in the evolutionary process. Targeting only one of them may then suffice to alter the tumour evolution. Therefore it is critical to have statistical methods which allow us to identify such pairs. GeneAccord is a novel statistical testing framework we developed especially to identify pairs of genes altered in distinct clones of the same tumour. Accounting for the evolutionary dependencies among clones emerged as critical to adequately control testing errors. In a cohort of 123 acute myeloid leukaemia patients, GeneAccord identified one clonally co-occurring and eight clonally exclusive gene pairs. The latter predominantly involved genes of key signalling pathways. [ABSTRACT FROM AUTHOR]