The Bayer process is the most frequently used method for the production of alumina from bauxite worldwide. The aim of the process is to grind and dissolve the alumina-rich minerals into hot caustic solution, than to separate the insoluble phases. These are followed by precipitation and calcination to produce alumina (Al2O3). After the crushing step the bauxite has to be ground usually in spent liquor at 60 ... 100 degrees C in a tumbling ball mill for dissolution. Due to the above special circumstances the determination of the specific grinding energy or the Bond work index for designing new grinding facilities and the optimization of the existing operations (grinding ball charge, filling ratio, revolution number, operating of classifier, etc ....) was not reliable when the traditional laboratory mills (Hardgrove-, Bond-. Zeisel mill) and procedures were used. To meet the requirements based on the standard grindability tests suitable methods and apparatuses were developed at the Institute of Raw Material Preparation and Environmental Process Engineering, University of Miskolc, called Universal Hardgrove- and Bond mill. This paper presents briefly these laboratory apparatuses and methods and shows the most important results of the systematic research work carried out recently concerning the grindability of lateritic and karst bauxites. Parallel experiments were performed using the Universal Hardgrove- and Bond mill and the measurement data were compared. The samples originated from three continents worldwide: Africa (Boke), Australia (Weipa) and Europe (Greece and Hungary). The results show good correlation between the developed methods. Temperature and caustic media are very important affecting parameters to the Bond work index, which can be demonstrated by the above mentioned developed laboratory mills and methods. (C) 2011 Elsevier B.V. All rights reserved.