  Quantum superpositions of coherent states are produced both in microwave and
optical domains, and are considered realizations of the famous "Schr\"odinger
cat" state. The recent progress shows an increase in the number of components
and the number of modes involved. Our work creates a theoretical framework for
treatment of multicomponent two-mode Schr\"odinger cat states. We consider a
class of single-mode states, which are superpositions of $N$ coherent states
lying on a circle in the phase space. In this class we consider an orthonormal
basis created by rotationally-invariant circular states (RICS). A two-mode
extension of this basis is created by splitting a single-mode RICS on a
balanced beam-splitter. We show that these states are generalizations of Bell
states of two qubits to the case of $N$-level systems encoded into
superpositions of coherent states on the circle, and we propose for them the
name of generalized quasi-Bell states. We show that using a state of this class
as a shared resource, one can teleport a superposition of coherent states on
the circle (a qudit). Differently from some other existing protocols of quantum
teleportation, the proposed protocol provides the unit fidelity for all input
states of the qudit. We calculate the probability of success for this type of
teleportation and show that it approaches unity for the average number of
photons in one component above $N^2$. Thus, the teleportation protocol can be
made unit-fidelity and deterministic at finite resources.
