This is the second part of the work on Geometry of curves in the Lagrange Grassmannians. Part I is published in Journal of Dynamical and Control Systems, Vol. 8, No. 1, 2002, pp. 93-104. Here we study an important class of flat curves and give the estimates for the conjugate points. The estimates are presented in the form of comparison theorems. We use terminology and notation introduced in Part I. In order to make references to Part I we write I before the number of the corresponding formula, section, theorem, proposition, or lemma from Part I.
