Ammonia, as a carbon-free fuel, holds promise as a potential alternative to fossil fuels. However, its practical implementation requires a comprehensive understanding of its combustion properties, particularly concerning flame stability. This study investigates the stability and flame appearance of partially premixed ammonia-methane flames in a concentric flow conical nozzle burner. The research explores the effects of varying the ammonia fraction in the inner stream, the outer stream velocity, and the degree of partial premixing (expressed as L/D). The findings indicate that flame stability is enhanced by increasing the outer stream equivalence ratio, while it is reduced by increasing the degree of premixing via higher L/D values. Notably, the case of L/D = 0 demonstrates a virtual improvement in flame stability, attributed to the absence of reaction between the inner mixture and the stable outer methane flame. This study provides valuable insights into the combustion characteristics of ammonia-methane blends under partially premixed conditions.