Customer relationship management and marketing analytics have become critical for non-life insurers operating in highly competitive markets. As it is easier to develop an existing customer than to acquire a new one, cross-selling and retention are key activities. In this research, we focus on both car and household-liability insurance products and consider the time a customer owning only a single product takes before buying the other product at the same insurer. Based on longitudinal consumer data from a Swiss insurance company covering the period from 2011 to 2015, we aim to study the factors driving the duration to cross-selling. Given the different dynamics observed in both products, we separately study the car and household-liability insurance customer cohorts. Considering the framework of survival analysis, we provide descriptive statistics and Kaplan-Meier estimates along major customer characteristics, contract history and distribution channel usage. For the econometric analysis of the duration, we compare the results from Cox and accelerated failure time models. We are able to characterize the times related to the buying behavior for both products through several covariates. Our results indicate that the policyholder age, the place of residence, the contract premium, the number of contracts held, and the initial access channel used for contracting influence the duration to cross-selling. In particular, our results underline the importance of the tied agent channel and the differences along the geographic region and the urbanicity of the place of residence. By quantifying the effects of the above factors, we extend the understanding of customer behavior and provide a basis for developing models to time marketing actions in insurance companies.