  Arbitrarily long lived modes, called quasi-resonances, are known to exist in
the spectrum of massive fields for a number of black-hole backgrounds at some
discrete values of mass of the field. Here we show that these modes also exist
in the background of wormholes, unless a wormhole has a constant red-shift
function, that is, tideless in the radial direction. The evidence of
quasi-resonances is supported by calculations in the frequency and time
domains, which are in a good concordance. At large masses of the field,
time-domain profiles of the absolute value of the wave function have peculiar
behavior: the long-lived modes dominate in the signal after a long period of
power-law tails.
