In this chapter we introduce the general class of symmetric two-qubit statesguaranteeing the perfect correlation or anticorrelation of Alice and Bob outcomeswhenever some spin observable is measured at both sites. It is proventhat, for all states from this class, the maximal violation of the original Bellinequality (OB) is upper bounded by 3/2 and specify the two-qubit stateswhere this quantum upper bound is attained. The case of two-qutrit statesis more complicated. Here, for all two-qutrit states, we obtain the same upperbound 3/2 for violation of the original Bell inequality under Alice and Bobspin measurements. But it has not yet been shown that this quantum upperbound is the least one. The experimental consequences of this mathematicalstudy are discussed.