  A linear operator $T$ between two lattice-normed locally solid Riesz spaces
is said to be $p_\tau$-continuous if, for any $p_\tau$-null net $(x_\alpha)$,
the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is also said to be
$p_\tau$-bounded operator if it sends $p_\tau$-bounded subsets to
$p_\tau$-bounded subsets. They are generalize several known classes of
operators such as continuous, order continuous, $p$-continuous, order bounded,
$p$-bounded operators, etc. We also study $up_\tau$-continuous operators
between lattice-normed locally solids Riesz spaces.
