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A wave phenomenon governed by solutions of Ìýa second order linear Ìýhyperbolic partial differential equation of normal hyperbolic type is said to satisfy Huygens' principle in the strict sense if the waves propagate sharply without a tail. Waves governed by the ordinary wave equation in three space dimensions have this property while the those in two dimensions do not. In 1923 Hadamard posed the problem, still unsolved, of determining all (generalized) wave equations with the Huygens' property. In this talk the current status of the problem in four independent variables will be reviewed Ìýand a new family of essentially non-self-adjoint Huygens' equations described.Ìý