Biosorption of copper ions by an industrial algal waste, from agar extraction industry has been studied in a batch system. This biosorbent was compared with the algae Gelidium itself, which is the raw material for agar extraction, and the industrial waste immobilized with polyacrylonitrile (composite material). The effects of contact time, pH, ionic strength (IS) and temperature on the biosorption process have been studied. Equilibrium data follow both Langmuir and Langmuir-Freundlich models. The parameters of Langmuir equilibrium model were: q(max)=33.0mgg(-1), K(L)=0.015mgl(-1); q(max)=16.7mgg(-1), K(L)=0.028mgl(-1) and q(max)=10.3mgg(-1), K(L)=0.160mgl(-1) respectively for Gelidium, algal waste and composite material at pH=5.3, T=20 degrees C and IS=0.001M. Increasing the pH, the number of deprotonated active sites increases and so the uptake capacity of copper ions. In the case of high ionic strengths, the contribution of the electrostatic component to the overall binding decreases, and so the uptake capacity. The temperature has little influence on the uptake capacity principally for low equilibrium copper concentrations. Changes in standard enthalpy, Gibbs energy and entropy during biosorption were determined. Kinetic data at different solution pH (3, 4 and 5.3) were fitted to pseudo-first-order and pseudo-second-order models. The adsorptive behaviour of biosorbent particles was modelled using a batch reactor mass transfer kinetic model, which successfully predicts Cu(II) concentration profiles.