Immunotherapy or Targeted Therapy With or Without Stereotactic Radiosurgery for Patients With Brain Metastases From Melanoma or Non-small Cell Lung Cancer

Most important inclusion criteria: * Newly diagnosed, previously untreated (except for surgery, see below) asymptomatic or oligo-symptomatic brain metastases, e.g., controlled symptomatic seizure disorder. Note: patients with neurological symptoms or signs that require more than a stable dose of 4 mg dexamethasone equivalent for more than one week are not considered oligo-symptomatic. * Requirements for brain metastases: * Brain metastases must be previously untreated, except for surgery. * Prior surgery (including biopsies, resection, and cyst aspiration) for brain metastases is allowed. Residual and measurable disease after surgery is not required, but surgery must have confirmed the diagnosis. An MRI performed within 72 hours post-surgery should be available. * Number and size of metastases at diagnosis of brain metastases: * Maximum 1-10 brain metastases at screening * At least one brain metastasis must be of ≥5 mm in diameter * In case of 1-4 brain metastases: * Longest diameter of largest brain metastasis must be ≤30 mm * In case of 5-10 brain metastases: * Largest metastasis must be ≤10 mL in volume and longest diameter must be ≤30 mm * Maximum cumulative brain metastases volume must be ≤30 mL * Primary disease of histologically confirmed (from primary tumour or from a metastatic lesion, including in the brain) melanoma or NSCLC * Requirements for patients with melanoma: * Prior treatment, including treatment with immune-checkpoint inhibitors is permitted, but brain metastases must be newly diagnosed and previously untreated (except for surgery). * BRAF-mutation status, locally assessed, should be known (previous adjuvant BRAF-targeted therapy is allowed). * Requirements for patients with NSCLC: * Newly diagnosed, treatment-naïve (except for prior surgery) metastatic NSCLC, with or without a targetable oncogenic driver alteration. * Known PD-L1 expression status (from primary tumour or from a metastatic lesion, including brain) * Known driver mutation status (from primary tumour or from a metastatic lesion, including brain). * Age of 18 years or older * Karnofsky performance status of 60 or more * Life expectancy \>12 weeks * Patients must be candidates for systemic treatment, within the defined cohorts (melanoma: cohorts 1a and 1b; NSCLC: cohorts 2a and 2b). * Women of childbearing potential, including women who had their last menstruation in the last 2 years, must have a negative urinary or serum pregnancy test within 7 days before randomisation. * Written IC for study participation must be signed and dated by the patient and the investigator prior to any study-related intervention. Most important exclusion criteria: * Confirmed or probable leptomeningeal metastases according to EANO ESMO criteria * Symptomatic brain metastases at time of randomisation, e.g., neurological symptoms or signs that require more than a stable dose of 4 mg dexamethasone equivalent for more than one week. * Patients must be off steroids or on a stable dose of ≤4 mg dexamethasone equivalent at randomisation. * Patients experiencing seizures controlled by anti-epileptic drugs are eligible. * Prior whole brain irradiation or focal radiation therapy to the brain * Prior systemic treatment for brain metastases * Contra-indication for SRS * Judgment by the investigator that the patient should not participate in the study if the patient is unlikely to comply with study procedures, restrictions and requirements. * Women who are pregnant or in the period of lactation. * Sexually active men and women of childbearing potential who are not willing to use an effective contraceptive method during the study.