An electric field and a magnetic field
exist in a region. The fields are not perpendicular to each other.
Explanation: There exists a mode of propagation of electromagnetic wave called the Transverse Electric and Magnetic (TEM) mode where both electric and magnetic field are moving tranverse to the direction of propagation of wave. The fields are not in the direction of propagation.
It is possible that an electromagnetic wave may exist when electric and magnetic fields are not perpendicular to each other.