Half-metallic Heusler alloys are among the most promising materials for future applications in spintronic devices. Although most Heusler alloys are ferromagnets, ferrimagnetic or antiferromagnetic (also called fully-compensated ferrimagnetic) alloys would be more desirable for applications due to the lower external fields. Ferrimagnetism can be either found in perfect Heusler compounds or achieved through the creation of defects in ferromagnetic Heusler alloys.Copyright line will be provided by the publisher Introduction : The family of the ferromagnetic Heusler alloys, e.g. NiMnSb or Co 2 MnSi, have been extensively studied during the last years due to their potential applications in magnetoelectronic devices [1]. Their main advantage with respect to other half-metallic systems is their structural similarity with the binary semiconductors and their high Curie temperatures. First principles calculations have been extensively employed to study their electronic and magnetic properties (see Refs. [2,3,4] and references therein). One of the most important features of these alloys is the Slater-Pauling behavior of their total spin magnetic moment which is given simply as a function of the number of valence electrons in the unit cell [5,6]. Authors have studied in the recent years several aspects of these half-metallic alloys like the properties of surfaces [7,8,9] and interfaces with semiconductors [10,11], the quaternary [12,13], the orbital magnetism [14,15], the effect of doping and disorder [16,17], the exchange constants [18] and the magneto-optical properties [19].Half-metallic ferrimagnetic Heusler alloys like Mn 2 VAl, where Mn and V atoms have antiparallel spin moments, are of particular interest since they create smaller external magnetic fields and thus lead to smaller energy losses [20,21]. In the extreme case like Cr 2 MnSb (alloys with 24 valence electrons) Cr and Mn spin moments cancel each other and the compounds are named as fully-compensated half-metallic ferrimagnets or simply half-metallic antiferromagnets [22]. Defects in these alloys show a very interesting behavior. When we substitute Co atoms with Cr(Mn) in the Co 2 Cr(Mn)Al and Co 2 Cr(Mn)Si compounds, the impurity atoms couple antiferromagnetically with the other transition metal atoms lowering the total spin moment [23,24]. Co and Fe impurities in Mn 2 VAl and Mn 2 VSi ferrimagnetic alloys have spin moments antiparallel to Mn and thus the total spin moment reaches closer to the zero value [25]. In this manuscript we will complete these studies presenting results for the Cr(Mn) impurites in ferromagnetic Co 2 Mn(Cr)Al and Co 2 Mn(Cr)Si alloys, the case of V and Cr impurities in ferrimagnetic Mn 2 VAl and Mn 2 VSi alloys and finally the 24-valence half-metallic antiferromagnetic alloys Cr 2 FeZ (Z= Si, Ge, Sn) using the full-potential nonorthogonal local-orbital band structure scheme (FPLO) [26].