  We investigate an event excess in the reaction $e^+p \to e^+ X$ with large
$x$ and high $Q^2$ observed at HERA and show that the events could naturally be
interpreted as a signature of the production of the scalar top quarks (stops)
in a supersymmetric model with $R$-parity breaking interactions. The HERA
events are characterized by the broad mass distribution and in fact it can be
simulated by our specific scenario if we consider almost degenerate two mass
eigenstates $\tilde{t_1}$ and $\tilde{t_2}$ of the stops.
