This is a double-blind, randomized, placebo-controlled crossover outpatient study in patients with peripheral neuropathic pain with allodynia or hyperalgesia to cold, heat, brush and/ or pinprick stimulation. Patients will in random order receive ACD440 Gel or placebo treatment twice daily for 7 days, topically applied to the painful area. This is followed by a 2-week washout period, then receive the alternate treatment.

Inclusion Criteria:

1. Signed informed consent prior to any study related procedures.
2. Male or female between 18 and 80 years of age, inclusive, at the screening visit.
3. Diagnosed with painful peripheral polyneuropathy (PNP), including etiologies behind the PNP being but not limited to painful peripheral polyneuropathy, peripheral mononeuropathy, postherpetic neuralgia (PHN), chemotherapy induced neuropathic pain, nerve injury pain, chronic postoperative neuropathic pain with a history of 6 months to 7 years prior to the screening visit.
4. Hypersensitivity to one or more of the following sensory stimuli: mechanical (brush or pinprick), thermal (cold).
5. Pain intensity of 4-7 out of 10 on a numerical rating scale (NRS) to any of the sensory stimuli mentioned in inclusion criterion
6. The area of sensory hypersensitivity can be up to a total of 600 cm2.
7. Subjects with reproductive potential will need to use accepted and highly effective means of contraception from study entry until at least 6 weeks for females (women of childbearing potential, WOCP) and 3 months for males after IMP discontinuation (as per the Clinical Trials Facilitation and Coordination Group (CTFG) guidelines).

Exclusion Criteria:

1. Participated in a clinical study and received active drug in such a study within 30 days or 5 study drug half-lives, whichever the longest, prior to screening visit.
2. A body mass index (BMI) <18.5 kg/m2 or >35 kg/m2.
3. Serum aspartate aminotransferase (ASAT) and alanine aminotransferase (ALAT) levels >2 times the upper limit of normal (ULN) at the screening assessments.
4. Evidence and/or history of any clinically significant neurological disease, other systemic diseases or conditions potentially interfering with study assessments, as judged by the investigator.
5. Have another concomitant pain condition with an intensity of ≥4 out of 10, for which, as judged by the principal investigator, pain ratings may interfere with study assessments.
6. Have a Hospital Anxiety and Depression Scale (HADS) score of 15 or above.
7. Active Human immunodeficiency virus (HIV) or ongoing hepatitis B and/or C.
8. Ongoing infection with fever (i.e., body temperature >38.0 ˚C).
9. Known history of hypersensitivity to components of the study drug or a history of anaphylactic reactions.
10. Malignancy within the past 5 years. In situ basal cell carcinoma and in situ squamous cell carcinoma of the skin are exempt, unless localised to the area of neuropathic pain.
11. History of dermatological diseases including rosacea, syphilitic and tuberculotic reactions.
12. Open wounds, scars, as well as extended tattoos on intended treatment areas.
13. Skin infections, acne, skin inflammation, eczema, or other dermatological disorders in the intended treatment area.
14. Pregnant or breastfeeding female or female who is planning pregnancy during the study period.
15. Could be negatively affected by participation in the study, as judged by the investigator.
16. Diagnosed with any significant psychiatric disorder according to Diagnostic and Statistical Manual of Mental Disorders (DSM) 5® criteria, including drug abuse or dependency.
17. Daily intake of opioids at a daily dose of more than 60 morphine equivalents.
18. Use of Lidocaine patches within 7 days prior to randomisation until the follow-up visit.
19. Use of Capsaicin patches within 4 months prior to randomisation until the follow-up visit.