  We compute the expected value of various quantities related to the
biparametric singularities of a pair of smooth centered Gaussian random fields
on an n-dimensional compact manifold, such as the lengths of the critical
curves and contours of a fixed index and the number of cusps. We obtain certain
expressions under no particular assumptions other than smoothness of the two
fields, but more explicit formulae are derived under varying levels of
additional constraints such as the two random fields being i.i.d, stationary,
isotropic etc.
