Anxiety is one of the most common comorbidities in youth with autism spectrum disorder (ASD), severely limiting academic opportunities and overall quality of life. In the present study, we compared several machine learning classifiers, namely support vector machine (SVM) and deep learning methods, in order to evaluate the feasibility of an EEG-based BCI for the real-time assessment and mitigation of anxiety through a closed-loop adaptation of respiration entrainment. We trained a total of eleven subject-dependent models—four with conventional BCI methods and seven with deep learning approaches—on the EEG of neurotypical (n=5) and ASD (n=8) participants performing alternating blocks of mental arithmetic stress induction, guided and unguided breathing. We propose a multiclass two-layer LSTM RNN deep learning classifier capable of identifying anxious states from ongoing EEG with an overall accuracy of 93.27%. Our study is the first to successfully apply an LSTM RNN classifier to identify anxious states from EEG in both neurotypical adolescents and adolescents with ASD.