Electronic bands belonging to the [20.4](3)Phi --> (1)(3)Delta System have been observed in the emission spectrum of lanthanum monofluoride at high temperature in the presence of the Ar+ 457.9-nm laser line: the (0-0), (1-1), (2-2), and (3-3) bands of the (3)Phi(4) -- > (3)Delta(3) subsystem and the (0-0) bands of the (3)Phi(3) --> (3)Delta(2) and (3)Delta(2) --> (3)Delta(1) subsystems. Rotational structures which are well developed in these experimental conditions were analyzed. The data were treated using a polynomial expression for the upper levels term-values, directly at equilibrium for (3)Phi(4), whereas a previous Hamiltonian matrix representation of the (1)(3)Delta state was assumed. A Hund's case (a) representation of the [20.4](3)Phi state at v = 0 was also considered. Perturbations affecting (3)Phi(2) levels at v = 0 were observed; the energy and rotational constant of the perturbing state and the interaction parameter were estimated. (C) 2002 Elsevier Science (USA).