Need method for analysing two sets of time course data

#1
Hello, I have two sets of time course data, they are for an eye-tracking study. The data is 20 100ms chunks, one category being percent fixations for canonical sentences, and the other being percent looks for non-canonical sentences. I would like to curve fit this (I believe the logistic curve would be the best fit), but also I want to look at things such as: when did one data set begin to asymptote with respect to the other and compare the growth rate and whatnot. Furthermore, I must know if these results are significant. I am using SPSS 20 to do my analysis. Any guidance into what direction I should be heading would be greatly appreciated! Cheers!