1. Informed oral and written consent

2. Diagnosed with schizophrenia according to the criteria of ICD-10 (International Classification of Diseases, World Health Organization (WHO)) or the DSM-V (Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition, the American Psychiatric Association)

3. Initiating current treatment with clozapine or olanzapine within 60 months (not PRN ordinations)

4. Age 18 years to 65 years (both included)

5. Body mass index (BMI) ≥25 kg/m2

6. Diagnosed with prediabetes or type 2 diabetes, after initiation of current treatment with clozapine- or olanzapine, with the following plasma levels: Prediabetes: HbA1c 35-47 mmol/mol or fasting plasma glucose (FPG) 5.6-6.9 mM or 2-h during 75 mg OGGT 7.8-11.0 mM. The test result has to be confirmed on a different day. Type 2 diabetes: HbA1c 48-57 mmol/mol or fasting plasma glucose (FPG) 6.9-9.9 mM or 2h OGTT > 11 mM (although FPG and HbA1c might still be under the diagnostic range). The test result has to be confirmed on a different day.

1. Acute worsening of psychosis based on a clinical evaluation (score of 6 or 7 on the CGI-S scale)

2. Coercive measures

3. Females of child-bearing potential who are pregnant, breast-feeding or have intention of becoming pregnant.

4. Women who are not willing to use adequate contraceptive during the full length of the study

5. Patients treated with corticosteroids or other hormone therapy (except oestrogens)

6. Any active substance abuse or dependence for the past six months (except for nicotine)

7. Impaired hepatic function (plasma liver transaminases >3 times upper normal limit)

8. Impaired renal function (serum creatinine >150 μmol/l and/or macroalbuminuria)

9. Impaired pancreatic function (acute or chronic pancreatitis and/or plasma amylase >2 times upper normal limit)

10. Cardiac problems defined as decompensated heart failure (NYHA class III/IV), unstable angina pectoris and/or myocardial infarction within the last 12 months

11. Hypertension with systolic blood pressure >180 mmHg or diastolic blood pressure >100 mmHg

12. Any condition that the investigator feels would interfere with trial participation

13. Receiving any experimental or pre-marketing drug within the last 3 months

14. Use of weight-lowering pharmacotherapy within the preceding 3 month

15. Known type 1 diabetes

16. Suicidal behavior as judged by the investigator and based on clinical evaluation. At all contact with patient attendance possible suicidality will be evaluated according to the guidelines. If the patient is evaluated as suicidal, the person will be excluded from the study and evaluated by a senior consultant in psychiatry, who will take further action.

17. Plasma HbA1c > 57 mmol/mol (tested twice) in which case the patient will be excluded from the study and transferred to general practitioner or hospital for diabetic treatment. No diabetic medication is allowed except for the trial medicin.

18. Any known contraindication towards the treatment with semaglutide.