We present electron spin resonance experiments in the one-dimensional antif
erromagnetic S=1 spin chains NENP and NINO in pulsed magnetic fields up to
50 T. The measured field dependence of the quantum energy gap for B\\b is a
nalyzed using the exact diagonalization method and the density matrix renor
malization group method. A staggered anisotropy term(-1)(i)d((SiSiz)-S-x (SiSix)-S-z) was considered in addition to a staggered field term (-1)(SiBs
t)-S-i-B-x. We show that the spin dynamics in high magnetic fields strongly
depends on the orthorhombic anisotropy E.