In the present study, speeded tasks with differing assumed difficulties of the trials are regarded as a special class of simple cognitive tasks. Exploratory latent growth modeling with data-driven shape of a growth curve and nonlinear structured latent curve modeling with predetermined monotonically increasing functions were used to analyze individual response-time change with an increase in task difficulty and to investigate latent response-time growth variables in relation to cognitive ability. A task that required participants to state the number of dots in a set was used as an example of a simple cognitive task with increasing difficulty; the response latencies obtained in this task and the magnitude of RT-IQ correlations changed depending on the complexity of the trial. Consistent with theoretical predictionsT, the individual speed of baseline performance was only weakly negatively correlated with each of the three measures of cognitive ability used in the study. The rate of change in response times with increasing task difficulty, estimated as a generalized growth parameter in the exploratory latent growth model, was significantly negatively related to cognitive ability. Response times of less intelligent individuals increased more rapidly in the task with increasing difficulty than the response times of highly intelligent individuals. Within the nonlinear structured latent curve modeling, the growth of response times with an increase in task difficulty was best described by a function that approached an oblique asymptote after an initial interval of convexity. A slope of this oblique asymptote was significantly negatively related to cognitive ability; for less intelligent individuals, the asymptote of response-time change was steeper than that for more intelligent individuals. In addition, a parameter that determined the shape of response-time growth trajectories on the interval of convexity was related to one of the three measures of cognitive ability. (Contains 4 tables and 4 figures.)