Undoubtedly, Customer Relationship Management (CRM) has gained its importance through the statement that acquiring a new customer is several times more costly than retaining and selling additional products to existing customers. Consequently, marketing practitioners are currently often focusing on retaining customers for as long as possible. However, recent findings in relationship marketing literature have shown that large differences exist within the group of long-life customers in terms of spending and spending evolution. Therefore, this paper focuses on introducing a measure of a customer's future spending evolution that might improve relationship marketing decision making. In this study, from a marketing point of view, we focus on predicting whether a newly acquired customer will increase or decrease his/her future spending from initial purchase information. This is essentially a classification task. The main contribution of this study lies in comparing and evaluating several Bayesian network classifiers with statistical and other artificial intelligence techniques for the purpose of classifying customers in the binary classification problem at hand. Certain Bayesian network classifiers have been recently proposed in the artificial intelligence literature as probabilistic white box classifiers which allow to give a clear insight into the relationships between the variables of the domain under study. We discuss and evaluate several types of Bayesian network classifiers and their corresponding structure learning algorithms. We contribute to the literature by providing experimental evidence that: (1) Bayesian network classifiers offer an interesting and viable alternative for our customer lifecycle slope estimation problem; (2) the Markov Blanket concept allows for a natural form of attribute selection that was very effective for the application at hand; (3) the sign of the slope can be predicted with a powerful and parsimonious general, unrestricted Bayesian network classifier; (4) a set of three variables measuring the volume of initial purchases and the degree to which customers originally buy in different categories, are powerful predictors for estimating the sign of the slope, and might therefore provide desirable additional information for relationship marketing decision making.