Exhibit 99.1

Alterity Therapeutics meeting with US FDA provides
development pathway for ATH434

MELBOURNE, AUSTRALIA AND SAN FRANCISCO, USA – 30th June 2020: Alterity Therapeutics (ASX: ATH, NASDAQ: ATHE) (“Alterity” or “the Company”) is pleased to announce that it has received guidance from the US Food and Drug Administration (FDA) in relation to the development pathway for ATH434 (previously PBT434), the company’s lead compound for the treatment of Multiple System Atrophy (MSA), a Parkinsonian disorder.

The company recently met with the FDA following the successful completion of its Phase 1 clinical trial last year and further data analysis. The pre-IND (Investigational New Drug) meeting was to obtain input on the clinical development plan for ATH434, including feedback on the Phase 2 study design.

Alterity reached agreement with the FDA on the non-clinical investigations required to support the Phase 2 study. In addition, the FDA agreed to key aspects of the Company’s Phase 2 study design including the proposed patient population, safety monitoring plan, and strategy for evaluating drug exposure during the study.

As there are currently no approved treatments for MSA and, therefore, no regulatory precedent regarding accepted efficacy endpoints, the FDA and Alterity will work together to develop an endpoint that is best suited for the MSA patients to be studied. The FDA has also encouraged Alterity to utilise data from a natural history study that Alterity has planned with clinical and neuroimaging experts at Vanderbilt University Medical Center in the US.

This natural history study, referred to as bioMUSE, or biomarkers of Progression in Multiple System Atrophy, will enroll early stage MSA patients and track change in clinical parameters and biomarkers for up to one year. Natural history studies are important for characterizing disease progression over time in selected patient populations. Well-conducted, these studies can provide vital information to optimize clinical trial design and inform the selection of biomarkers to evaluate target engagement of drug candidates.

In parallel with the US strategy, Alterity is also pursuing a regulatory pathway in Europe and Australia. Given the uncertainty of study conduct and recruitment in the COVID-19 era, and with the need to target sites that are minimally impacted, it is prudent for the Company to be flexible in identifying and recruiting sites around the world and maintaining optionality. Planning is already underway to meet with European authorities.

Dr David Stamler, Chief Medical Officer, said: “The FDA clearly recognizes the seriousness of MSA and the need for new treatments to address this devastating Orphan disease. Our pre-IND meeting was very collegial, and I look forward to again collaborating with the Division of Neurology to determine the best development path for ATH434 in the US. With the information obtained from this meeting, we have a clear path forward for conducting our Phase 2 study in MSA.”

END

Authorization & Additional information

This announcement was authorized by Geoffrey Kempler, CEO and Chairman of Alterity Therapeutics Limited.

Contact:

Investor Relations

Rebecca Wilson, WE Communications

E: WE-AUAlterity@we-worldwide.com

Tp: +61 3 8866 1216

About Alterity Therapeutics Limited and ATH434

Alterity’s lead candidate, ATH434 (formerly PBT434), is the first of a new generation of small molecules designed to inhibit the aggregation of pathological proteins implicated in neurodegeneration. ATH434 has been shown to reduce abnormal accumulation of α-synuclein and tau proteins in animal models of disease by redistributing labile iron in the brain. In this way, it has potential to treat Parkinson’s disease and atypical forms of Parkinsonism such as Multiple System Atrophy (MSA) and Progressive Supranuclear Palsy (PSP).

ATH434 has been granted Orphan designation for the treatment of MSA by the US FDA and the European Commission.

For further information please visit the Company’s web site at www.alteritytherapeutics.com.

About Multiple System Atrophy

Multiple System Atrophy (MSA) is a rare and rapidly progressive neurological disorder affecting adults. It has no known cause. In addition to presenting with motor symptoms like those in Parkinson’s disease, individuals with MSA may also experience loss of ability to coordinate voluntary movements and impaired regulation of involuntary body functions such as blood pressure, bowel and bladder control. Most of these symptoms are not addressed by available drugs for patients with Parkinson’s disease. As the condition progresses, daily activities become increasingly difficult and complications such as increased difficulty swallowing, vocal cord paralysis, progressive immobility, and poor balance become more prominent. Symptoms tend to appear after age 50 and rapidly advance, leading to profound disability.

Forward Looking Statements

This press release contains "forward-looking statements" within the meaning of section 27A of the Securities Act of 1933 and section 21E of the Securities Exchange Act of 1934. The Company has tried to identify such forward-looking statements by use of such words as "expects," "intends," "hopes," "anticipates," "believes," "could," "may," "evidences" and "estimates," and other similar expressions, but these words are not the exclusive means of identifying such statements.

Important factors that could cause actual results to differ materially from those indicated by such forward-looking statements are described in the sections titled “Risk Factors” in the Company’s filings with the SEC, including its most recent Annual Report on Form 20-F as well as reports on Form 6-K, including, but not limited to the following: statements relating to the Company's drug development program, including, but not limited to the initiation, progress and outcomes of clinical trials of the Company's drug development program, including, but not limited to, ATH434 (formerly PBT434), and any other statements that are not historical facts. Such statements involve risks and uncertainties, including, but not limited to, those risks and uncertainties relating to the difficulties or delays in financing, development, testing, regulatory approval, production and marketing of the Company’s drug components, including, but not limited to, ATH434, uncertainties relating to the impact of the novel coronavirus (COVID-19) pandemic on the company’s business, operations and employees, the ability of the Company to procure additional future sources of financing, unexpected adverse side effects or inadequate therapeutic efficacy of the Company's drug compounds, including, but not limited to, ATH434, that could slow or prevent products coming to market, the uncertainty of patent protection for the Company's intellectual property or trade secrets, including, but not limited to, the intellectual property relating to ATH434.

Any forward-looking statement made by us in this press release is based only on information currently available to us and speaks only as of the date on which it is made. We undertake no obligation to publicly updated any forward-looking statement, whether written or oral, that may be made from time to time, whether as a result of new information, future developments or otherwise.