  We introduce nonlinear scalar field models for open and open-closed strings
with spacetime derivatives encoded in the operator valued Riemann zeta
function. The corresponding two Lagrangians are derived in an adelic approach
starting from the exact Lagrangians for effective fields of $p$-adic tachyon
strings. As a result tachyons are absent in these models. These new strings we
propose to call zeta strings. Some basic classical properties of the zeta
strings are obtained and presented in this paper.
