Abstract <p> In this paper, the asymptotics of the fundamental solution of a degenerate parabolic equation with a small parameter at the highest derivative is constructed. It is shown that the leading term of the asymptotics contains two phase functions, which is not typical for linear problems. Estimates are provided that relate the leading term of the asymptotics in the general case to the exact solution in the trivial case. The asymptotics is constructed in the form of a formal series in powers of the small parameter. The asymptotics is justified by proving the convergence of the obtained series. </p> <p> <b> DOI</b> 10.1134/S1061920825600722 </p>