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Two types of boundary conditions ("soliton preserving" and "solitonnon-preserving") are investigated for the sl(n) and sl(m|n) open spin chains.The appropriate reflection equations are formulated and the correspondingsolutions are classified. The symmetry and the Bethe Ansatz equations arederived for each case. The general treatment for non-diagonal reflectionmatrices associated to "soliton preserving" case is worked out. The connectionbetween the "soliton non-preserving" boundary conditions and the twisted(super) Yangians is also discussed.Comment: 37 page

General boundary conditions for the and open spin chains