Yes, nuts naturally contain sugar. Whilst not really thought of as an inherently sugary food, nuts naturally contain a small amount of sugar (around 2-6g/100g) in the form sucrose.

Nuts contain natural sugars and depending on the nut variety, contain between 2.1 and 5.9g sugars per 100g. Pistachios contain the most sugar (5.9g/100g) and Brazil nuts the least (2.1g/100g). The type of sugar found naturally in nuts is sucrose – the same type that is in sugar cane and crystallised as white, brown or raw sugar. 

Despite their natural sugar content, nuts help to reduce the glycaemic index of a meal, and the glycaemic load of the diet [1, 2]. The protein, healthy fats and fibre content of nuts helps to slow their digestion.