In the yeast Hansenula polymorpha an oxygen-requiring enzyme, alcohol oxidase, catalyzes the conversion of methanol into formaldehyde. After growth on methanol cells of the organism were harvested and entrapped in barium-alginate gels. The diffusion of oxygen towards these cells is seriously hindered by the polymer network. This caused significant changes in the kinetics of methanol oxidation by the immobilized cells as compared to that observed with cells free in suspension. The apparent K~(O2) of the immobilized cells was dependent upon the density of the cells in the alginate beads and the bead radius. Using a well-known theoretical model, originally developed to describe the kinetics of oxygen diffusion in mold pellets, the diffusion coefficient for oxygen in barium-alginate gels was estimated. This coefficient was only 25% of that in water. The model also allowed an adequate simulation of the observed kinetics of methanol oxidation by the immobilized cells.List of Symbols C, local oxygen concentration inside the alginate bead; tool -cm-3; C, external oxygen concentration; tool -cm -3" D(O:)~g, diffusion constant for oxygen in a barium-alginate matrix; era 2 9 s-l; Ks(O2) , Michaelis-Menten constant for oxygen at excess (200 raM) methanol; raM; p, ratio of D(Oz)alg over O(O2)water; Qo2, rate of oxygen consumption by free cells (at C = C); tool 9 s -1 , g-1 cells; 002, rate of oxygen consumption by the alginate beads; tool. s -t. g-i cells; Q(32 rate of oxygen consumption by immobilized cells (at C = C); tool 9 s -1 -g 1 cells; Q'o2 maximum rate of oxygen consumption; tool 9 s t . g-1 cells; R, radius of an alginate bead; cm; r, radial distancc; x, dimensionless radius (r/R); y, dimensionless oxygen concentration (C/s ct, Thiele modulus given by Eq. 5; fl, dimensionless Micbaelis-Mxnten constant for oxygen [Ks(02)/O ] ; l,~, cell density of an alginate bead; g cells, cm -3 alginate beads; r] effectiveness factor given by Eq. 7 Offprint requests to: W. Harder containing per dm 3 of deionized water: (NH02SO4, 2.5g; MgSO4.7 H20 , 0.2g; NaI-IzPO4, 3,0 g; K2HPO4, 0.7 g; yeast extract, 0.5 g; trace elements solution (Vishniac and Santer 1957),