We report the first observation of persistent photoconductivity (PPC) in In1-xGaxAsyP1-y epilayers. The decay behaviour of PPC is similar to that in AlxGa1-xAs and can be well described by a stretch-exponential function. The origin of PPC is discussed in terms of several models. Under the excitation-energy, temperature and alloy-composition dependence of the PPC effects, it is found the lattice relaxation of DX-like impurity is responsible for PPC in In1-xGaxAsyP1-y. Our results indicate that PPC in In1-xGaxAsyP1-y has a similar origin as that in AlxGa1-xAs. However, the decay-time constant and electron-capture barrier in In1-xGaxAsyP1-y are about 11 orders of magnitude and 46% smaller than those in AlxGa1-xAs, respectively.