  The $\mu \nu$SSM proposes to use right-handed neutrino supermultiplets in
order to generate the $\mu$ term and neutrino masses simultaneously. We discuss
neutrino physics and the associated electroweak seesaw mechanism in this model.
We show how to obtain, from the neutralino-neutrino mass matrix of the $\mu
\nu$SSM, the effective neutrino mass matrix. In particular we discuss certain
limits of this matrix that clarify the neutrino-sector behavior of the model.
We also show that current data on neutrino masses and mixing angles can easily
be reproduced. These constraints can be fulfilled even with a diagonal neutrino
Yukawa matrix, since this seesaw does not involve only the right-handed
neutrinos but also the MSSM neutralinos. To obtain the correct neutrino angles
turns out to be easy due to the following characteristics of this seesaw:
R-parity is broken and the relevant scale is the electroweak one.
