AbstactBose-Einstein condensate of magnons (mBEC) that is formed at room temperature in parametrically pumped magnetic films is double-degenerate: it is formed simultaneously in two spectral minima corresponding to the lowest energy magnons propagating in opposite directions along the in-plane bias magnetic field. In this work the interactions of magnons in the mBEC are studied both theoretically and experimentally. It is shown by direct calculation that the magnons residing in each of the degenerate spectral minima of mBEC form a practically ideal magnon gas, as the attractive self-interaction between these magnons is very weak. At the same time, the interaction between the magnons residing in different spectral minima, corresponding to the opposite directions of the magnon wave vector, is relatively strong and repulsive, leading to a repulsive total inter-magnon interaction. By measuring the spectral characteristics of the mBEC it is shown, that with the increased magnon density the energy per magnon in the mBECs increases, thus confirming experimentally that the net inter-magnon interaction in a doubledegenerate mBEC is repulsive.