This paper is concerned with derivation of a complete Hamiltonian and its r
ovibronic part containing no anomalous (singular) coefficients like I-alpha
/2(I-beta-I-gamma)(2) by the square components of the orbital angular momen
tum for an N-particle system. The work consists of two parts. In the first
part the reasons for appearance of the anomalies (in earlier papers [1,2] a
s well as in more recent ones [4-9]) are analyzed and a general procedure o
f removing the singularities is proposed through the correct consideration
of both determination of the angular momentum and mutual displacements of t
he particles. The complete description of transition from laboratory variab
les to molecular ones including non-holonomic coordinates is presented. In
the second part the explicit expressions of the Hamiltonians are obtained t
hrough the use of tensor methods. The first of them is as follows: [GRAPHIC
] Here P-alpha, L-alpha, P-k are the components of the total momentum, the
angular momentum and momenta of internal motion.