Summary: Suppose \(X\) and \(Y\) are locally solid vector lattices. A linear operator \(T:X\to Y\) is said to be \(nb\)-compact provided that there exists a zero neighborhood \(U\subseteq X\), such that \(\overline{T(U)}\) is compact in \(Y\); \(T\) is \(bb\)-compact if for each bounded set \(B\subseteq X\), \(\overline{T(B)}\) is compact. These notions are far from being equivalent, in general. In this paper, we introduce the notion of a locally solid \(AM\)-space as an extension for \(AM\)-spaces in Banach lattices. With the aid of this concept, we establish a variant of the known Krengel’s theorem for different types of compact operators between locally solid vector lattices. This extends [C. D. Aliprantis and O. Burkinshaw, Positive operators. Reprint of the 1985 original. Berlin: Springer (2006; Zbl 1098.47001), Theorem 5.7] (established for compact operators between Banach lattices) to different classes of compact operators between locally solid vector lattices.