A ternary linear recurrence

is of Berstel type if it satisfies the recurrence relation

for all

. In this paper, we investigate the zero-multiplicity
of such sequences. We prove that, except for nonzero multiples of shifts of the Berstel sequence with initial values

, which has zero-multiplicity 6, and nonzero multiples of shifts of the sequence
with initial values

, which has zero-multiplicity 3, all other sequences have zero multiplicity at most 2.