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.
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