Magnetic order has been investigated in stripe-ordered La(2-x)Sr(x)NiO(4) (x = 0.275, 0.37, 0.4) by d.c. magnetization and by polarized- and unpolarized-neutron diffraction. In the magnetically ordered phase, all three compositions exhibit a magnetic transition consistent with a spin reorientation in the ab plane. For x = 0.37, the spin axes rotate from an angle of 37.7 +/- 0.3 degrees to the stripe direction at 71 K, to 52.3 +/- 0.2 degrees at 2 K. The x = 0.275 and 0.4 compounds were found to

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... undergo a similar spin reorientation. A spin reorientation has now been observed to occur for five different doping levels in the range x = 0.275 - 0.5, suggesting that this spin transition is an intrinsic property of the stripe phase.