  Aims. To date, more than 600 multi-planetary systems have been discovered.
Due to the limitations of the detection methods, our knowledge of the systems
is usually far from complete. In particular, for planetary systems discovered
with the radial velocity (RV) technique, the inclinations of the orbital
planes, and thus the mutual inclinations and planetary masses, are unknown. Our
work aims to constrain the spatial configuration of several RV-detected
extrasolar systems that are not in a mean-motion resonance. Methods. Through an
analytical study based on a first-order secular Hamiltonian expansion and
numerical explorations performed with a chaos detector, we identified ranges of
values for the orbital inclinations and the mutual inclinations, which ensure
the long-term stability of the system. Our results were validated by comparison
with n-body simulations, showing the accuracy of our analytical approach up to
high mutual inclinations (approx. 70{\deg}-80{\deg}). Results. We find that,
given the current estimations for the parameters of the selected systems,
long-term regular evolution of the spatial configurations is observed, for all
the systems, i) at low mutual inclinations (typically less than 35{\deg}) and
ii) at higher mutual inclinations, preferentially if the system is in a
Lidov-Kozai resonance. Indeed, a rapid destabilisation of highly mutually
inclined orbits is commonly observed, due to the significant chaos that
develops around the stability islands of the Lidov-Kozai resonance. The extent
of the Lidov-Kozai resonant region is discussed for ten planetary systems (HD
11506, HD 12661, HD 134987, HD 142, HD 154857, HD 164922, HD 169830, HD 207832,
HD 4732, and HD 74156).
