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Let us consider a signed measure $\Qv$ and a probability measure $\Pv$ suchthat $\Qv<<\Pv$. Let $D$ be the density of $\Qv$ with respect to $\Pv$. $H$represents the set of zeros of $D$, $\bar{g}=0\vee\sup{H}$. In this paper, weshall consider two classes of nonnegative processes of the form$X_{t}=N_{t}+A_{t}$. The first one is the class of semimartingales where $ND$is a cadlag local martingale and $A$ is a continuous and non-decreasing processsuch that $(dA_{t})$ is carried by $H\cup\{t: X_{t}=0\}$. The second one is thecase where $N$ and $A$ are null on $H$ and $A_{.+\bar{g}}$ is a non-decreasing,continuous process such that $(dA_{t+\bar{g}})$ is carried by  $\{t: X_{t+\bar{g}}=0\}$. We shall show that these classes are extensions ofthe class $(\sum)$ defined by A.Nikeghbali \cite{nik} in the framework ofstochastic calculus for signed measures.

New classes of processes in stochastic calculus for signed measures