  Three sets of ladder operators in spheroconal coordinates and their
respective actions on Lam\'e spheroconal harmonic polynomials are presented in
this article. The polynomials are common eigenfunctions of the square of the
angular momentum operator and of the asymmetry distribution Hamiltonian for the
rotations of asymmetric molecules, in the body-fixed frame with principal axes.
The first set of operators for Lam\'e polynomials of a given species and a
fixed value of the square of the angular momentum raise and lower and lower and
raise in complementary ways the quantum numbers $n_1$ and $n_2$ counting the
respective nodal elliptical cones. The second set of operators consisting of
the cartesian components $\hat L_x$, $\hat L_y$, $\hat L_z$ of the angular
momentum connect pairs of the four species of polynomials of a chosen kind and
angular momentum. The third set of operators, the cartesian components $\hat
p_x$, $\hat p_y$, $\hat p_z$ of the linear momentum, connect pairs of the
polynomials differing in one unit in their angular momentum and in their
parities. Relationships among spheroconal harmonics at the levels of the three
sets of operators are illustrated.
