Abstract: We introduce a class of new interior-point algorithms (IPA) for solving sufficient linear complementarity problems (LCP). The algebraic equivalent transformation (AET) technique is used to determine the search directions. We introduce a whole new class of AET functions, which differs from the classes used earlier in the literature of IPAs to define search directions. We give an example of an AET function from the new class whose corresponding kernel function is not a self-regular and a traditional kernel function. We prove that the interior-point algorithm using any member of the new class of AET functions determines an approximate solution in polynomial time in the size of the problem, in starting point’s duality gap, in the accuracy parameter and in the special parameter (handicap) of the sufficient matrix. Joint work with Petra R. Rigó and Roland Török.