A type of fixed bed or fluidized bed reactor in which living microbial cells or enzymes are held statically such that their movement is restricted. Depending on the characteristics of the cells or enzymes, they may be immobilized in the form of aggregates such as pellets, or adhere to porous structures such as diatomaceous earth, glass, dextran, and gelatine, or be entrapped within beads such as calcium alginate. The advantage of immobilization is that high oxygen transfer rates can be achieved and the cells can be protected from high shear forces. Cell washout can also be avoided.