  The angular correlation of the electrons emitted in the neutrinoless double
beta decay ($0\nu2\beta$) is presented using a general Lorentz invariant
effective Lagrangian for the leptonic and hadronic charged weak currents. We
show that the coefficient $K$ in the angular correlation $d\Gamma/d\cos \theta
\propto (1-K\cos \theta)$ is essentially independent of the nuclear matrix
element models and present its numerical values for the five nuclei of interest
($^{76}{Ge}$, $^{82}{Se}$, $^{100}{Mo}$, $^{130}{Te}$, and $^{136}{Xe}$),
assuming that the $0\nu2\beta$-decays in these nuclei are induced solely by a
light Majorana neutrino, $\nu_M$. This coefficient varies between $K=0.81$ (for
the $^{76}{Ge}$ nucleus) and $K=0.88$ (for the $^{82}{Se}$ and $^{100}{Mo}$
nuclei), calculated taking into account the effects from the nucleon recoil,
the $S$ and $P$-waves for the outgoing electrons and the electron mass.
Deviation of $K$ from its values derived here would indicate the presence of
New Physics (NP) in addition to a light Majorana neutrino, and we work out the
angular coefficients in several $\nu_M + {NP}$ scenarios for the $^{76}{Ge}$
nucleus. As an illustration of the correlations among the $0\nu2\beta$
observables (half-life $T_{1/2}$, the coefficient $K$, and the effective
Majorana neutrino mass $|< m>|$) and the parameters of the underlying NP model,
we analyze the left-right symmetric models, taking into account current
phenomenological bounds on the right-handed $W_R$-boson mass and the left-right
mixing parameter $\zeta$.
