Azimuthal distributions of pi+, K+, and K- mesons have been measured in Au+Au reactions at 1.5A GeV and Ni+Ni reactions at 1.93 A GeV. In semicentral collisions at midrapidity, pi+ and K+ mesons are emitted preferentially perpendicular to the reaction plane in both collision systems. In contrast for K- mesons in Ni+Ni reactions, an in-plane elliptic flow was observed for the first time at these incident energies.