A function f meromorphic on ℂ\ℝ is said to be in the generalized Nevanlinna class N κ (κ ϵ ℤ+), if f is symmetric with respect to ℝ and the kernel $$ {\mathbf{N}}_{\omega }(z)\coloneq \frac{f(z)-\overline{f\left(\omega \right)}}{z-\overline{\omega}} $$ has κ negative squares on ℂ+. The generalized Stieltjes class $$ {\mathbf{N}}_{\kappa}^k\left(\kappa, k\in {\mathrm{\mathbb{Z}}}_{+}\right) $$ is defined as the set of functions f ϵ N κ such that z f ϵ N k . The full indefinite Stieltjes moment problem $$ {MP}_{\kappa}^k\left(\mathbf{s}\right) $$ consists in the following: Given κ, k ϵ ℤ+, and a sequence $$ \mathbf{s}={\left\{{s}_i\right\}}_{i=0}^{\infty } $$ of real numbers, to describe the set of functions $$ f\in {\mathbf{N}}_{\kappa}^k $$ , which satisfy the asymptotic expansion $$ f(z)=-\frac{s_0}{z}-\cdots -\frac{s_2n}{z^{2n+1}}+o\left(\frac{1}{z^{2n+1}}\right)\kern1em \left(z=-y\in {\mathrm{\mathbb{R}}}_{-},y\uparrow \infty \right) $$ for all n big enough. In the present paper, we will solve the indefinite Stieltjes moment problem $$ {MP}_{\kappa}^k\left(\mathbf{s}\right) $$ within the M. G. Krein theory of u-resolvent matrices applied to a Pontryagin space symmetric operator A [0;N] generated by $$ {\mathfrak{J}}_{\left[0;N\right]} $$ . The u-resolvent matrices of the operator A [0;N] are calculated in terms of generalized Stieltjes polynomials, by using the boundary triple’s technique. Some criteria for the problem $$ {MP}_{\kappa}^k\left(\mathbf{s}\right) $$ to be solvable and indeterminate are found. Explicit formulae for Pade approximants for the generalized Stieltjes fraction in terms of generalized Stieltjes polynomials are also presented.