In the present article, it is argued that in addition to the traditional ra
ndom generation tasks discussed by Towse and Neil (1998), random time inter
val generation tasks should be considered as useful alternatives, because t
hey allow a better empirical control of the executive task component in dua
l-task situations. First, a framework for discussing randomness over time i
s presented. Then, the article goes on to present three methods for the ana
lysis of such tasks. A first method is based on the correlation between the
intervals produced. The second method calculates the approximate entropy,
and the third method converts the time sequences into binary sequences and
estimates the statistical properties of the sequence on the basis of these
binary data. A principal components analysis on 19 different measures based
on 1,381 sequences produced in a number of single-task and dual-task exper
iments shows that the proposed measures form two general clusters, one rela
ted to output probability, perseveration, and alternation, and one related
to sequential commonalities. The article also briefly describes a computer
program that implements these methodologies.