Summary: The authors extend the \(Q\)-superlinear convergence theory recently developed by \textit{Y. Zhang}, \textit{R. A. Tapia} and \textit{J. E. Dennis} [SIAM J. Optim. 2, No. 2, 304-324 (1992; Zbl 0763.90066)] for a class of interior-point linear programming algorithms to similar interior-point algorithms for quadratic programming and for linear complementarity problems. This unified approach consists of viewing all these algorithms as a damped Newton method applied to perturbations of a general problem. A set of sufficient conditions for these algorithms to achieve \(Q\)- superlinear convergence is established. The key ingredients consist of asymptotically taking the step to the boundary of the positive orthant and letting the centering parameter approach zero at a specific rate. The construction of algorithms that have both the global property of polynomiality and the local property of superlinear convergence will be the subject of further research.