  In this article, we study the Iwasawa theory for cuspidal automorphic
representations of $\mathrm{GL}(n)\times\mathrm{GL}(n+1)$ over CM fields along
anticyclotomic directions, in the framework of the Gan-Gross-Prasad conjecture
for unitary groups. We prove one-side divisibility of the corresponding Iwasawa
main conjecture: when the global root number is $1$, the $p$-adic $L$-function
belongs to the characteristic ideal of the Iwasawa Bloch-Kato Selmer group;
when the global root number is $-1$, the square of the characteristic ideal of
a certain Iwasawa module is contained in the characteristic ideal of the
torsion part of the Iwasawa Bloch-Kato Selmer group (analogous to Perrin-Riou's
Heegner point main conjecture).
