  We introduce the notion of linear multifractional stable sheets in the broad
sense (LMSS) with $\alpha\in(0,2]$, to include both linear multifractional
Brownian sheets ($\alpha=2$) and linear multifractional stable sheets
($\alpha<2$). The purpose of the present paper is to study the existence and
joint continuity of the local times of LMSS, and also the local H\"older
condition of the local times in the set variable. Among the main results of
this paper, Theorem 2.4 provides a sufficient and necessary condition for the
existence of local times of LMSS; Theorem 3.1 shows a sufficient condition for
the joint continuity of local times; and Theorem 4.1 proves a sharp local
H\"older condition for the local times in the set variable. All these theorems
improve significantly the existing results for the local times of
multifractional Brownian sheets and linear multifractional stable sheets in the
literature.
