A method is disclosed for separating a substance from a liquid medium. The method comprises combining the liquid medium containing the substance with magnetic particles under conditions for non-specific chemical binding of the magnetic particles. Thereafter, the medium is subjected to a magnetic field gradient to separate the particles from the medium. The preferred non-specific binding is achieved as the result of charge interactions between the particles usually by means of a polyionic reagent. The method of the invention has particular application to the separation of cells and microorganisms from aqueous suspensions and also to the determination of an analyte in a sample suspected of containing the analyte. The analyte is a member of a specific binding pair (sbp). The sample is combined in an assay medium with magnetic particles and a sbp member complementary to the analyte. Magnetic or non-magnetic particles capable of specific binding to the analyte or its complementary sbp member must be included in the assay medium. The combination is made under conditions for non-specifically aggregating the magnetic particles or coaggregating the magnetic and non-magnetic particles when non-magnetic particles are present. The assay medium is subjected to a magnetic field gradient to separate the aggregated particles from the medium. Then, the medium or the particles are examined for the presence or amount of the analyte or an sbp member, the binding of which is affected by the presence of the analyte.