Schizophrenia and obsessive-compulsive disorder (OCD) affect ~3% of the population. The illnesses often begin in adolescence. Approximately 1/3 of patients are treatment-resistant, i.e. no known treatment is effective. These people have extremely low function, quality of life and a shortened life. Family members are also severely affected. Patients also have a higher incidence of physical diseases, especially autoimmune ones. While immunological diseases are traditionally associated with physical illness, recent research has shown that mental illness can also be explained by inflammation in the brain. Rituximab is a well-proven anti-inflammatory drug used in several autoimmune diseases. It consists of antibodies that block the function of a type of cell (B cells) that is part of the body's immune system. It inhibits the immune system. We will investigate whether severely ill and treatment-resistant adults with schizophrenia or OCD improve with rituximab. The treatment will take place on one occasion, then participants will be followed regularly for one year to evaluate the effect. The evaluations will be done using established evaluation instruments. We will also examine signs of inflammation in blood, spinal fluid, feces and brain (using brain imaging) before and after treatment to look for biological markers that can give us guidance on causality. If effective, treatment with rituximab could eventually revolutionize the understanding and treatment of these patient groups.