  In this note, we consider special algebraic cycles on the Shimura variety S
associated to a quadratic space V over a totally real field F, |F:\Q|=d, of
signature ((m,2)^{d_+},(m+2,0)^{d-d_+}), 1\le d_+<d. For each n, 1\le n\le m,
there are special cycles Z(T) in S, of codimension nd_+, indexed by totally
positive semi-definite matrices with coefficients in the ring of integers O_F.
The generating series for the classes of these cycles in the cohomology group
H^{2nd_+}(S) are Hilbert-Siegel modular forms of parallel weight m/2+1. One can
form analogous generating series for the classes of the special cycles in the
Chow group CH^{nd_+}(S). For d_+=1 and n=1, the modularity of these series was
proved by Yuan-Zhang-Zhang. In this note we prove the following: Assume the
Bloch-Beilinson conjecture on the injectivity of Abel-Jacobi maps. Then the
Chow group valued generating series for special cycles of codimension nd_+ on S
is modular for all n with 1\le n\le m.
