We calculate the field dependence of dynamical structure factors of the S = 1 bondalternating Heisenberg-chain compound Ni(C9D24N4)(NO2)ClO4 and the S = 1 Haldanegap compound Ni(C5D14N2)2N3(PF6). We show that in the former system the highest magnon branch vanishes at H ∼ 0.63Hc and one gapped branch emerges in H > Hc, where Hc is the critical field for the energy-gap closing. In the latter system, by contrast, three distinct magnon branches appear below and above Hc. The results are in qualitative agreement with recent experimental findings.