  The string theory on symmetric product describes the second-quantized string
theory. The development for the bosonic open string was discussed in the
previous work. In this paper, we consider the open superstring theory on the
symmetric product and examine the nature of the second quantization. The
fermionic partition functions are obtained from the consistent fermionic
extension of the twisted boundary conditions for the non-abelian orbifold, and
they can be interpreted in terms of the long string language naturally. In the
closed string sector, the boundary/cross-cap states are also constructed. These
boundary states are classified into three types in terms of the long string
language, and explain the change of the topology of the world-sheet. To obtain
the anomaly-free theory, the dilaton tadpole must be cancelled. This condition
gives SO(32) Chan-Paton group as ordinary superstring theory.
