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We say that a $C^*$-algebra $\\cl A$ satisfies the similarity property ((SP) for short) if every bounded homomorphism $u\\colon \\cl A\\to \\cl B(H)$ is similar to a $*$-homomorphism and that a von Neumann algebra $\\cl A$ satisfies the weak similarity property ((WSP) for short) if every $\\mathrm{w}^*$-conitnuous unital and bounded homomorphism $u\\colon \\cl A\\to \\cl B(H),$ where $H$ is a Hilbert space, is similar to a $*$-homomorphism. 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