The aim of this project is to establish new analytical and numerical stability results for physiologically structured population models, in particular models describing cell populations, for example stem cell differentiation and quiescence models. We formulate models as delay equations and apply functional analytic methods to establish new well-posedness, linearized stability and Hopf-bifurcation results for the class of equations induced by our models. We adapt and extend numerical continuation methods and compute existence and stability boundaries in parameter planes for new structured population models. To our knowledge this is the first application of, both analytical and numerical delay equation methods in cell population modelling.