  We discuss the vacuum structure of $\phi^4$-theory in 1+1 dimensions
quantised on the light-front $x^+ =0$. To this end, one has to solve a
non-linear, operator-valued constraint equation. It expresses that mode of the
field operator having longitudinal light-front momentum equal to zero, as a
function of all the other modes in the theory. We analyse whether this zero
mode can lead to a non-vanishing vacuum expectation value of the field $\phi$
and thus to spontaneous symmetry breaking. In perturbation theory, we get no
symmetry breaking. If we solve the constraint, however, non-perturbatively,
within a mean-field type Fock ansatz, the situation changes: while the vacuum
state itself remains trivial, we find a non-vanishing vacuum expectation value
above a critical coupling. Exactly the same result is obtained within a
light-front Tamm-Dancoff approximation, if the renormalisation is done in the
correct way.
