The bound states of n Frenkel excitons (n=2, 3,...), which are called excitonic n-strings, are theoretically shown to exist in contrast with a system of Wannier excitons. The electronic structure and nonlinear optical responses of these excitonic n-strings are clarified. The first evidence for the excitonic 2- and 3-strings is provided from comparison of the calculated and observed differential transmission spectrum of an Anthracene-PMDA crystal pumped by femtosecond laser pulses.