Ensuring the authenticity of horse-, donkey- and pig-related meat products is of great religious and economic significance. In this study, with the mitochondrial genes of ATPase 6 or ND2 as targets, the species-specific real-time enzymatic recombinase amplification (real-time ERA) and ERA combined with lateral flow strip (LFS ERA) assays for horse, donkey and pig ingredients were developed. The optimization results showed that both ERA assays had the same optimal temperature for the detection of horse, donkey and pig ingredients, i.e., 39 °C for real-time ERA and 37 °C for LFS ERA, respectively. The assays could be performed simultaneously and the results could obtained within 25 min. Both developed assays showed good specificity and no cross-reactions with other common meat species were observed. The limit of detection of the developed ERA assays for horse, donkey and pig ingredients was 10 pg genomic DNA/per reaction and 0.1% target meat (w/w). Their applicability were verified with 45 donkey meat products (both raw and marinated minced meat), and the results showed that the detection rate of horse or pig ingredient was as high as 53.33%, including a complete substitution or partial substitution of donkey meat. The results were consistent with those of the standard real-time PCR in China, but the whole detection time was significantly reduced from 2 h to 35 min. It is concluded that the developed real-time ERA and LFS ERA assays are feasible for the rapid authentication of horse, donkey and pig meats and identification of the adulteration of donkey meat-related products.