  The critical state of a thin superconducting strip in an oblique applied
magnetic field H_a is analyzed without any restrictions on the dependence of
the critical current density j_c on the local magnetic induction {\bf B}. In
such a strip, j_c is not constant across the thickness of the sample and
differs from J_c/d, where J_c is the critical sheet current. It is shown that
in contrast to the case of {\bf B}-independent j_c, the profiles H_z(x) of the
magnetic-field component perpendicular to the strip plane generally depend on
the in-plane component H_{ax} of the applied magnetic field H_a, and on how H_a
is switched on. On the basis of this analysis, we explain how and under what
conditions one can extract j_c({\bf B}) from the magnetic-field profiles H_z(x)
measured by magneto-optical imaging or by Hall-sensor arrays at the upper
surface of the strip.
