  A genuine continuum treatment of the massive \phi^4_{1+1}-theory in
light-cone quantization is proposed. Fields are treated as operator valued
distributions thereby leading to a mathematically well defined handling of
ultraviolet and light cone induced infrared divergences and of their
renormalization. Although non-perturbative the continuum light cone approach is
no more complex than usual perturbation theory in lowest order. Relative to
discretized light cone quantization, the critical coupling increases by 30% to
a value r = 1.5. Conventional perturbation theory at the corresponding order
yields r_1=1, whereas the RG improved fourth order result is r_4 = 1.8 +-0.05.
