Studies on neurofeedback (for ADHD, Asperger's, ASD) referenced by nih pubmed:

- "Efficacy of neurofeedback treatment in ADHD: the effects on inattention, impulsivity and hyperactivity: a meta-analysis" Clin EEG Neurosci 2009 Netherlands http://www.ncbi.nlm.nih.gov/pubmed/19715181
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prospective controlled studies and studies employing a pre- and post-design ... neurofeedback treatment for ADHD can be considered "Efficacious and Specific" (Level 5) with a large ES for inattention and impulsivity and a medium ES for hyperactivity

- "Neurofeedback outcomes in clients with Asperger's syndrome" Appl Psychophysiol Biofeedback 2010 Canada http://www.ncbi.nlm.nih.gov/pubmed/19908142
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150 clients with Asperger's Syndrome (AS) and 9 clients with Autistic Spectrum Disorder (ASD) seen over a 15 year period (1993-2008) in a clinical setting ...

gain for the Full Scale IQ score was 9 points ... positive outcomes of decreased symptoms of Asperger's and ADHD (including a decrease in difficulties with attention, anxiety, aprosodias, and social functioning) plus improved academic and intellectual functioning, provide preliminary support for the use of neurofeedback as a helpful component of effective intervention in people with AS.

(Pardon a layman's question - does nih pubmed reference only peer-reviewed studies?)

There is also a review re. ASD:

- "Neurofeedback for autistic spectrum disorder: a review of the literature" Appl Psychophysiol Biofeedback 2010 US http://www.ncbi.nlm.nih.gov/pubmed/19856096

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noninvasive approach shown to enhance neuroregulation and metabolic function in ASD