Low-lying horocycles are known to equidistribute on the modular curve. Here we consider the joint distribution of two low-lying horocycles of different speeds in the product of two modular curves and show equidistribution under certain necessary diophantine conditions. The techniques involve a combination of multiplicative number theory and ergodic theory. This is joint work with Valentin Blomer (and this abstract was written by Blomer and used without permission).