The problem of Intervalizing Colored Graphs has received a lot of attention due to their use as a model for DNA physical mapping with ambiguous data. If k is the number of colors, the problem is known to be NP-Complete for general graphs for kgeq 4 and has polynomial time algorithms for k=2 and k=3. In this paper we prove that the problem is NP-Complete for caterpillars with hairs of length at most 2. In the positive side we give polynomial time algorithms for the problem in the cases, caterpillars with hairs of length at most 1 and any number of colors and caterpillars with hairs of length at most 2 and a constant number of colors. It is the first time a problem has been shown NP-complete for the particular case of caterpillars of hairs of length at most 2.