  We discuss some new simple closed bosonic string solutions in AdS_5 x S^5
that may be of interest in the context of AdS/CFT duality. In the first part of
this work we consider solutions with two spins (S_1, S_2) in AdS_5. Starting
from the flat-space solutions and using perturbation theory in the curvature of
AdS_5 space, we construct leading terms in the small two-spin solution. We find
corrections to the leading Regge term in the classical string energy and
uncover a discontinuity in the spectrum for certain type of a solution. We then
analyze the connection between small-spin and large-spin limits of string
solutions in AdS_5. We show that the S_1 = S_2 solution in AdS_5 found in
earlier papers admits both limits only in simplest cases of the folded and
rigid circular strings. In the second part of the paper we construct a new
class of chiral solutions in R_t x S^5 for which embedding coordinates of S^5
satisfy the linear Laplace equations. They generalize the previously studied
rigid string solutions. We study in detail a simple nontrivial example.
