  We present electron spin resonance experiments in the one-dimensional
antiferromagnetic S=1 spin chains NENP and NINO in pulsed magnetic fields up to
50T. The measured field dependence of the quantum energy gap for B||b is
analyzed using the exact diagonalization method and the density matrix
renormalization group method (DMRG). A staggered anisotropy term (-1)^i d(S_i^x
S_i^z + S_i^z S_i^x) was considered for the first time in addition to a
staggered field term (-1)^i S_i^x B_st. We show that the spin dynamics in high
magnetic fields strongly depends on the orthorhombic anisotropy E.
