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The Notch pathway plays a vital role in determining whether cells in the intestinal epithelium adopt a secretory or an absorptive phenotype. Cell fate specification is coordinated via Notch’s interaction with the canonical Wnt pathway. Here, we propose a new mathematical model of the Notch and Wnt pathways, in which the Hes1 promoter acts as a hub for pathway crosstalk. Computational simulations of the model can assist in understanding how healthy intestinal tissue is maintained, and predict the likely consequences of biochemical knockouts upon cell fate selection processes. Chemical reaction network theory (CRNT) is a powerful, generalised framework which assesses the capacity of our model for monostability or multistability, by analysing properties of the underlying network structure without recourse to specific parameter values or functional forms for reaction rates. CRNT highlights the role of β-catenin in stabilising the Notch pathway and damping oscillations, demonstrating that Wnt-mediated actions on the Hes1 promoter can induce dynamic transitions in the Notch system, from multistability to monostability. Time-dependent model simulations of cell pairs reveal the stabilising influence of Wnt upon the Notch pathway, in which β-catenin- and Dsh-mediated action on the Hes1 promoter are key in shaping the subcellular dynamics. Where Notch-mediated transcription of Hes1 dominates, there is Notch oscillation and maintenance of fate flexibility; Wnt-mediated transcription of Hes1 favours bistability akin to cell fate selection. Cells could therefore regulate the proportion of Wnt- and Notch-mediated control of the Hes1 promoter to coordinate the timing of cell fate selection as they migrate through the intestinal epithelium and are subject to reduced Wnt stimuli. Furthermore, mutant cells characterised by hyperstimulation of the Wnt pathway may, through coupling with Notch, invert cell fate in neighbouring healthy cells, enabling an aberrant cell to maintain its neighbours in mitotically active states., Author summary Epithelial cells which line the intestine form finger-shaped structures called crypts; these undergo a process of renewal at the base, causing cells to migrate upwards until they die and are sloughed off into the gut. Much of our understanding of how crypts function rests upon two processes: proliferation, in which cells divide to produce ‘daughter cells’; and differentiation, in which cells become progressively more specialised as they migrate along the crypt axis and mature. Coordinated proliferation and differentiation enable each crypt to renew itself and to produce a range of specialised cell types essential to its healthy functioning. In this paper we build a mathematical model for two reaction pathways which regulate proliferation and differentiation. We use this model to explore how crosstalk between these pathways in cell pairs influences the generation of distinct cell fates in intestinal tissues. By modifying our model to represent abnormal, ‘mutant’ cells, we investigate abnormalities typical of early colorectal cancer. Computational simulation of our model identifies an important region of crosstalk in our reaction network which determines whether cells adopt the same fate as one another, or different fates. Our model may prove useful for realistic simulations of whole crypts in the future.