Background: Multiple myeloma is an incurable haematological malignancy, representing over 10% of haematological cancers in the USA. We did a phase 1–2 study of melflufen and dexamethasone in patients with relapsed and refractory multiple myeloma to determine the maximum tolerated dose of melflufen and to investigate its safety and efficacy. Methods: We did a multicentre, international, dose-confirmation and dose-expansion, open-label, phase 1–2 study in seven centres in the USA and Europe. Eligible patients were aged 18 years or older, had relapsed and refractory multiple myeloma, had received two or more previous lines of therapy (including lenalidomide and bortezomib), were refractory to their last line of therapy, and had an Eastern Cooperative Oncology Group performance status of 2 or less. In phase 1, patients received an intravenous infusion of melflufen at 15 mg, 25 mg, 40 mg, or 55 mg for 30 min on day 1 in 21-day cycles plus oral dexamethasone 40 mg weekly and did not receive melflufen as a single agent. Melflufen was also tested in a single-agent cohort late in phase 2 in a small number of patients at the maximum tolerated dose identified in phase 1. In phase 2, patients were enrolled at the maximum tolerated dose in the melflufen plus dexamethasone in the combination cohort. The phase 1 primary objective was to determine the maximum tolerated dose. The phase 2 primary objective was to evaluate overall response rate and clinical benefit rate. This primary analysis was done per protocol, in the all-treated and efficacy-evaluable population (defined as patients who received at least two doses of melflufen and who had a response assessment after baseline). The single-agent melflufen cohort was closed on October 6, 2016, as per the recommendation by the data safety monitoring committee on the basis of interim data suggesting greater activity in the melflufen plus dexamethasone cohort. The study is completed but survival follow-up is ongoing. This study is registered with ClinicalTrials.gov, NCT01897714. Findings: Patients were enrolled between July 4, 2013, and Dec 31, 2016: 23 patients in phase 1 and 58 in phase 2, including six patients from phase 1 treated at the maximum tolerated dose of melflufen 40 mg plus weekly dexamethasone. In phase 2, 45 patients were given a combination of melflufen plus dexamethasone and 13 patients were given single-agent melflufen. In phase 1, the established maximum tolerated dose was 40 mg of melflufen in combination with dexamethasone. No dose-limiting toxicities were observed in the first three dose cohorts (15 mg, 25 mg, and 40 mg). The highest dose cohort tested (55 mg) exceeded the maximum tolerated dose because four of six patients experienced grade 4 neutropenia with grade 4 thrombocytopenia also occurring in three of these patients; therefore, the planned highest dose of 70 mg was not tested. In phase 2, patients treated with combination therapy achieved an overall response rate of 31% (14 of 45 patients; 95% CI 18–47) and clinical benefit rate of 49% (22 of 45; 34–64) in the all-treated population, and 41% (14 of 34; 25–59) and 65% (22 of 34; 47–80) in the efficacy-evaluable population. In the phase 2 single-agent cohort, the overall response rate was 8% (one of 13 patients; 0·2–36·0) and the clinical benefit rate was 23% (three of 13; 5–54). Among the 45 patients given melflufen plus dexamethasone during phase 2, the most common grade 3–4 adverse events were clinically manageable thrombocytopenia (28 [62%] patients) and neutropenia (26 [58%]), and non-haematological toxicity was infrequent. 24 serious adverse events were reported in 17 (38%) of 45 patients, most commonly pneumonia (five [11%]). The most common grade 3–4 adverse events that occurred in the phase 2 single-agent cohort of 13 patients were neutropenia (nine [69%]) and thrombocytopenia (eight [62%]). Nine patients experienced serious adverse events in the single-agent cohort, most commonly thrombocytopenia (two [15%]). There were three deaths from adverse events within 30 days of treatment that were possibly related to treatment: one in the 25 mg cohort in phase 1 (due to bacteraemia) and two in the phase 2 combination cohort (one due to neutropenic sepsis and one due to Escherichia coli sepsis), each in the setting of progressive disease. Interpretation: These data show that melflufen is active in patients with relapsed and refractory multiple myeloma and tolerable in most patients. These results show the feasibility of this regimen and support the initiation of additional clinical studies of melflufen in multiple myeloma, both in combination with dexamethasone as well as in triplet regimens with additional classes of drugs. Funding: Oncopeptides AB.