We studied the relative importance of residence time, propagule pressure, and species traits in three stages of invasion of alien woody plants cultivated for about 150 years in the Czech Republic, Central Europe. The probability of escape from cultivation, naturalization, and invasion was assessed using classification trees. We compared 109 escaped-not-escaped congeneric pairs, 44 naturalized-not-naturalized, and 17 invasive-not-invasive congeneric pairs. We used the following predictors of the above probabilities: date of introduction to the target region as a measure of residence time; intensity of planting in the target area as a proxy for propagule pressure; the area of origin; and 21 species-specific biological and ecological traits. The misclassification rates of the naturalization and invasion model were low, at 19.3% and 11.8%, respectively, indicating that the variables used included the major determinants of these processes. The probability of escape increased with residence time in the Czech Republic, whereas the probability of naturalization increased with the residence time in Europe. This indicates that some species were already adapted to local conditions when introduced to the Czech Republic. Apart from residence time, the probability of escape depends on planting intensity (propagule pressure), and that of naturalization on the area of origin and fruit size; it is lower for species from Asia and those with small fruits. The probability of invasion is determined by a long residence time and the ability to tolerate low temperatures. These results indicate that a simple suite of factors determines, with a high probability, the invasion success of alien woody plants, and that the relative role of biological traits and other factors is stage dependent. High levels of propagule pressure as a result of planting lead to woody species eventually escaping from cultivation, regardless of biological traits. However, the biological traits play a role in later stages of invasion.