We study here the behavior of nonspacelike geodesics in dust collapse model
s in order to understand the causal structure of the spacetime. The geodesi
c families coming out, when the singularity is naked, corresponding to diff
erent initial data are worked out and analyzed. We also bring out the simil
arity of the limiting behavior for different types of geodesics in the Limi
t of the approach to the singularity.