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We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras$\mathcal{A}_b$ arising from a one-to-one correspondence between the sets ofrelations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$in AdS$_d$-spaces and the sets of operators that form $\mathcal{A}$ and$\mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic,$s_i=n_i$, $n_i \in \mathbb{N}_0$, $i=1,2$, HS fields characterized by a Youngtableaux with two rows. We consider a method of constructing the Verma modules$V_\mathcal{A}$, $V_{\mathcal{A}_b}$ for $\mathcal{A}$, $\mathcal{A}_b$ andestablish a possibility of their Fock-space realizations in terms of formalpower series in oscillator operators which serve to realize an additiveconversion of the above (super)algebra ($\mathcal{A}$) $\mathcal{A}_b$,containing a set of 2nd-class constraints, into a converted (super)algebra$\mathcal{A}_{b{}c}$ = $\mathcal{A}_{b}$ + $\mathcal{A}'_b$ ($\mathcal{A}_c$ =$\mathcal{A}$ + $\mathcal{A}'$), containing a set of 1st-class constraintsonly. For the algebra $\mathcal{A}_{b{}c}$, we construct an exact nilpotentBFV--BRST operator $Q'$ having nonvanishing terms of 3rd degree in the powersof ghost coordinates and use $Q'$ to construct a gauge-invariant Lagrangianformulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) andgeneralized spin $\mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraicconstraints are examined as well.

Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian Description of Mixed-symmetry HS Fields in AdS Spaces