[For part I see ibid. 89, No. 2, 161-180 (2001; see the preceding review Zbl 1021.13014).] Let \((R,{\mathfrak m})\) be a local ring, and let \(X = X_\bullet\) be a bounded \(R\)-complex with finitely generated homology modules. The Cohen-Macaulay defect \(\text{cmd}_R X\) of \(X\) is defined by \(\text{cmd}_R X = \dim_R X - \text{depth}_R X\), and \(X\) is said to be Cohen-Macaulay if \(\text{cmd}_R X = 0\). In this section 2 of the paper supports of complexes are studied and the notion of an anchor prime ideal is introduced. A prime ideal \(p\) of \(R\) is said to be an anchor prime ideal for a bounded below \(R\)-complex \(Y\) if \(p \in \text{Supp}_R Y\) and \(\dim_{R_p}Y_p + \inf Y_p = 0\). Corollary 2.4. If \(p \in \text{Ass}_R X\) is an anchor prime ideal for \(X\), then \(\text{cmd}_{R_p} X_p = \sup X_p - \inf X_p\). Theorem 2.9. \(\dim_R X + \inf X = \inf\{ s \mid \exists a_1, \dots,a_s \text{ such that } {\mathfrak m} \text{ is an anchor prime ideal for }\) \(K(a_1, \dots,a_s;X) \}\). (\(K(\;;\;)\) is the Koszul complex.) Let \( d = \dim_R X + \inf X\). A sequence of elements \(\mathbf x = x_1, \ldots,x_d \in {\mathfrak m}\) is said to be a system of parameters for \(X\) if \({\mathfrak m}\) is an anchor prime ideal for \(K(\mathbf x;X)\), and an \(X\)-parameter sequence is part of a system of parameters for \(X\). For a bounded above complex \(Y\), we put \(z_R(Y) = z_R(H_{\sup Y}(Y))\) (the set of zero divisors). A sequence of elements \(\mathbf y = y_1, \ldots,y_n\) is said to be a \(Y\)-sequence if (i) \(y_j \notin z_R K(\mathbf y_{j-1};Y)\) for \(1 \leq j \leq n\), (ii) \(K(\mathbf y;Y) \not\simeq 0\) or \(Y \simeq 0\). In section 3, several theorems concerning \(X\)-parameter sequences and the Cohen-Macaulay defect are shown, and the following theorem is given: Theorem 3.9. Let \(C\) be a Cohen-Macaulay semi-dualizing complex for \(R\) and \(\mathbf y = y_1, \dots,y_n\) a sequence of elements in \({\mathfrak m}\). Suppose \(X\) is \(C\)-reflexive. Then \(\mathbf y\) is an \(X\)-parameter sequence if and only if it is an \(R\Hom_R(X,C)\)-sequence.