Responses to items from an intelligence test may be fast or slow. The research issue dealt with in this paper is whether the intelligence involved in fast correct responses differs in nature from the intelligence involved in slow correct responses. There are two questions related to this issue: 1. Are the processes involved different? 2. Are the abilities involved different? An answer to these questions is provided making use of data from a Raven-like matrices test and a verbal analogies test, and the use of a psychometric branching model. The branching model is based on three latent traits: speed, fast accuracy and slow accuracy, and item parameters corresponding to each of these. The pattern of item difficulties is used to draw conclusions on the cognitive processes involved. The results are as follows: 1. The processes involved in fast and slow responses can be differentiated, as can be derived from qualitative differences in the patterns of item difficulty, and fast responses lead to a larger differentiation between items than slow responses do. 2. The abilities underlying fast and slow responses can also be differentiated, and fast responses allow for a better differentiation between the respondents. (Contains 1 figure and 2 tables.)