An anti-icing system of a nacelle inlet of an engine of an aircraft, wherein the anti-icing system comprises: a valve assembly (66; 100) fluidly connected to the nacelle inlet, wherein the valve assembly (60; 100) comprises: a first direct acting valve comprising: a first inlet; a first valve chamber fluidly connected to the first inlet; a first upstream wall, wherein the first valve chamber is bounded in an upstream direction by the first upstream wall; a first internal valve body circumferentially surrounding the first valve chamber; a first outlet; and a first piston for adjusting a rate of flow (W I) of air through the first direct acting valve, wherein the first piston is slidably engaged with the first internal valve body; a first control valve assembly fluidly connected to the first valve chamber of the first direct acting valve; a second direct acting valve comprising: a second inlet; a second valve chamber fluidly connected to the second inlet; a second upstream wall wherein the second valve chamber is bounded in an upstream direction by the second upstream wall; a second internal valve body circumferentially surrounding the second valve chamber; a second outlet; and a second piston for adjusting a rate of flow of air (W PR) through the second direct acting valve, wherein the second piston is slidably engaged with the second internal valve body, and further wherein the second direct acting valve is fluidly connected to the first direct acting valve in a series configuration such that the second inlet of the second direct acting valve is directly connected to the first outlet of the first direct acting valve; and a second control valve assembly fluidly connected to the second valve chamber of the second direct acting valve; characterized in that the first direct active valve comprises a first hole positioned on the first upstream wall, wherein the first hole fluidly connects the first inlet with the first valve chamber; and in that the second direct acting valve comprises a second hole positioned on the second upstream wall, wherein the second hole fluidly connects the second inlet with the second valve chamber. a first direct acting valve comprising: a first inlet; a first valve chamber fluidly connected to the first inlet; a first upstream wall, wherein the first valve chamber is bounded in an upstream direction by the first upstream wall; a first internal valve body circumferentially surrounding the first valve chamber; a first outlet; and a first piston for adjusting a rate of flow (W I) of air through the first direct acting valve, wherein the first piston is slidably engaged with the first internal valve body; a first inlet; a first valve chamber fluidly connected to the first inlet; a first upstream wall, wherein the first valve chamber is bounded in an upstream direction by the first upstream wall; a first internal valve body circumferentially surrounding the first valve chamber; a first outlet; and a first piston for adjusting a rate of flow (W I) of air through the first direct acting valve, wherein the first piston is slidably engaged with the first internal valve body; a first control valve assembly fluidly connected to the first valve chamber of the first direct acting valve; a second direct acting valve comprising: a second inlet; a second valve chamber fluidly connected to the second inlet; a second upstream wall wherein the second valve chamber is bounded in an upstream direction by the second upstream wall; a second internal valve body circumferentially surrounding the second valve chamber; a second outlet; and a second piston for adjusting a rate of flow of air (W PR) through the second direct acting valve, wherein the second piston is slidably engaged with the second internal valve body, and further wherein the second direct acting valve is fluidly connected to the first direct acting valve in a series configuration such that the second inlet of the second direct acting valve is directly connected to the first outlet of the first direct acting valve; and a second inlet; a second valve chamber fluidly connected to the second inlet; a second upstream wall wherein the second valve chamber is bounded in an upstream direction by the second upstream wall; a second internal valve body circumferentially surrounding the second valve chamber; a second outlet; and a second piston for adjusting a rate of flow of air (W PR) through the second direct acting valve, wherein the second piston is slidably engaged with the second internal valve body, and further wherein the second direct acting valve is fluidly connected to the first direct acting valve in a series configuration such that the second inlet of the second direct acting valve is directly connected to the first outlet of the first direct acting valve; and a second control valve assembly fluidly connected to the second valve chamber of the second direct acting valve; characterized in that the first direct active valve comprises a first hole positioned on the first upstream wall, wherein the first hole fluidly connects the first inlet with the first valve chamber; and in that the second direct acting valve comprises a second hole positioned on the second upstream wall, wherein the second hole fluidly connects the second inlet with the second valve chamber.