  In this paper, we derive general conditions for a shadow to occur, without a
photon sphere in a spacetime, caused by central nulllike or timelike naked
singularities. Using these conditions, we propose classes of spacetimes which
have nulllike and timelike naked singularities at the center, and that fulfill
these `shadow without photon sphere' conditions. Considering additional
asymptotically flat conditions, we show that, for a fixed Schwarzschild mass,
the timelike naked singularities can cast a shadow of a size that is equal to,
greater or smaller, than the size of a black hole shadow. On the other hand,
the size of shadow of a nulllike naked singularity is always less than that of
a black hole. Such novel features of shadows of nulllike and timelike naked
singularities in the absence of photon spheres may help us to distinguish
between black holes and naked singularities observationally.
