We are concerned with $\mathcal K$-manifolds which are a natural generalization of metric quasi-Sasakian ma\-ni\-folds. They are Riemannian manifolds with a compatible $f$-stru\-ctu\-re which admits a parallelizable kernel, have closed Sasaki 2-form and verify a certain normality condition. We study semi-invariant submanifolds of a $\cal K$-manifold and investigate the integrability of the various distributions involved. We also study the normality of semi-invariant submanifolds and present a significant example.