Summary: The SDLCP (semidefinite linear complementarity problem) in symmetric matrices introduced in this paper provides a unified mathematical model for various problems arising from systems and control theory and combinatorial optimization. It is defined as the problem of finding a pair \((X,Y)\) of \(n\times n\) symmetric positive semidefinite matrices which lies in a given \(n(n+1)/2\)-dimensional affine subspace \(\mathcal F\) of \({\mathcal S}^2\) and satisfies the complementarity condition \(X\bullet Y=0\), where \(\mathcal S\) denotes the \(n(n+1)/2\)-dimensional linear space of symmetric matrices and \(X\bullet Y\) the inner product of \(X\) and \(Y\). The problem enjoys a close analogy with the LCP in the Euclidean space. In particular, the central trajectory leading to a solution of the problem exists under the nonemptiness of the interior of the feasible region and a monotonicity assumption on the affine subspace \(\mathcal F\). The aim of this paper is to establish a theoretical basis of interior-point methods with the use of Newton directions toward the central trajectory for the monotone SDLCP.