Conventional magnetic separators are only able to split the feeding stream into three different outcome streams. This work presents the theoretical principles of a new device, named MAGCLA (TM), which is capable to separate and classify particles according to their magnetic susceptibility. This first part of the work reports the equations of movement for non-magnetic particles. The equations for magnetic particles and the limiting conditions for both situations will be given in the remaining parts of this work. A coefficient (T-CGI) was introduced to measure the deviations between the experimental and theoretical values. (c) 2006 Elsevier B.V. All rights reserved.