<p>We present a method for bidirectional teleportation of a single qubit using quantum walks on two independent one-dimensional lattices and two independent cycles with four vertices, employing nearest-neighbor jumps with coin outcomes. In addition, we discuss two different methods for two-qubit teleportation by employing nearest-neighbor jumps and next-nearest-neighbor jumps with a single coin and two coins, respectively. Finally, it is demonstrated that the two-qubit single-jump and the two-jump quantum walk teleportation schemes yield the same results.</p>